inquanto.computables¶
inquanto.computables.atomic¶
Submodule for quantum computable expressions that interact directly with InQuanto Protocols.
 class ExpectationValue(state, kernel)¶
Bases:
ComputableNode
[float
]Represents the expectation value of a Hermitian operator kernel with a state.
\(\langle \Psi  H  \Psi\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Input state.kernel (
QubitOperator
) – Hermitian operator kernel.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueBraDerivativeImag(state, kernel, symbols)¶
Bases:
IExpectationValueDerivative
Represents the imaginary part of the bra derivatives of an expectation value of a Hermitian operator.
\(\Im \langle\partial_{\theta} \Psi(\theta)  H  \Psi(\theta)\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).kernel (
QubitOperator
) – Qubit operator kernel \(H\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueBraDerivativeReal(state, kernel, symbols)¶
Bases:
IExpectationValueDerivative
Represents the real part of the bra derivatives of an expectation value of a Hermitian operator.
\(\Re \langle \partial_{\theta} \Psi(\theta)  H  \Psi(\theta)\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).kernel (
QubitOperator
) – Qubit operator kernel \(H\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueDerivative(state, kernel, symbols)¶
Bases:
IExpectationValueDerivative
Represents the derivatives of the expectation value of a Hermitian operator.
\(\partial_{\theta} \langle \Psi(\theta)  H  \Psi(\theta) \rangle\)
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).kernel (
QubitOperator
) – Qubit operator kernel \(H\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueKetDerivativeImag(state, kernel, symbols)¶
Bases:
IExpectationValueDerivative
Represents the imaginary part of the ket derivatives of an expectation value of a Hermitian operator.
\(\Im \langle\Psi(\theta)  H  \partial_{\theta} \Psi(\theta)\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).kernel (
QubitOperator
) – Qubit operator kernel \(H\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueKetDerivativeReal(state, kernel, symbols)¶
Bases:
IExpectationValueDerivative
Represents the real part of the ket derivatives of an expectation value of a Hermitian operator.
\(\Re \langle\Psi(\theta)  H  \partial_{\theta} \Psi(\theta)\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).kernel (
QubitOperator
) – Qubit operator kernel \(H\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class ExpectationValueNonHermitian(state, kernel)¶
Bases:
ComputableNode
[complex
]Represents the expectation value of a nonHermitian operator kernel with a state.
\(\langle \Psi  H  \Psi\rangle\)
 Parameters:
state (
GeneralAnsatz
) – Input state.kernel (
QubitOperator
) – Operator kernel.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
QubitOperator
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class MetricTensorImag(state, symbols)¶
Bases:
IMetricTensor
Represents the imaginary part of the metric tensor.
Calculates: \(\Im \langle\partial_{\theta_i} \Psi(\theta)  \partial_{\theta_j}\Psi(\theta)\rangle\) for all \(i, j\).
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class MetricTensorReal(state, symbols)¶
Bases:
IMetricTensor
Represents the real part of the metric tensor.
Calculates: \(\Re \langle\partial_{\theta_i} \Psi(\theta)  \partial_{\theta_j}\Psi(\theta)\rangle\) for all \(i, j\).
 Parameters:
state (
GeneralAnsatz
) – Ansatz state \(\Psi(\theta)\rangle\).symbols (
Set
[Symbol
]) – Symbols with respect to which the derivatives are computed.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:

state:
GeneralAnsatz
¶
 class Overlap(bra_state, ket_state, kernel=<factory>)¶
Bases:
IOverlap
Represents the overlap of two states with a Hermitian kernel operator.
\(\langle\Phi  H  \Psi\rangle\)
 Parameters:
bra_state (
GeneralAnsatz
) – Bra state \(\Phi\rangle\).ket_state (
GeneralAnsatz
) – Ket state \(\Psi\rangle\).kernel (
Union
[QubitOperator
,QubitOperatorString
], default:<factory>
) – Qubit operator kernel \(H\).
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.

bra_state:
GeneralAnsatz
¶
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
Union
[QubitOperator
,QubitOperatorString
]¶

ket_state:
GeneralAnsatz
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class OverlapImag(bra_state, ket_state, kernel=<factory>)¶
Bases:
IOverlap
Represents the imaginary part of the overlap of two states with a Hermitian kernel operator.
\(\Im \langle\Phi  H  \Psi\rangle\)
 Parameters:
bra_state (
GeneralAnsatz
) – Bra state \(\Phi\rangle\).ket_state (
GeneralAnsatz
) – Ket state \(\Psi\rangle\).kernel (
Union
[QubitOperator
,QubitOperatorString
], default:<factory>
) – Qubit operator kernel \(H\).
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.

bra_state:
GeneralAnsatz
¶
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
Union
[QubitOperator
,QubitOperatorString
]¶

ket_state:
GeneralAnsatz
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class OverlapReal(bra_state, ket_state, kernel=<factory>)¶
Bases:
IOverlap
Represents the real part of the overlap of two states with a Hermitian kernel operator.
\(\Re \langle\Phi  H  \Psi\rangle\)
 Parameters:
bra_state (
GeneralAnsatz
) – Bra state \(\Phi\rangle\).ket_state (
GeneralAnsatz
) – Ket state \(\Psi\rangle\).kernel (
Union
[QubitOperator
,QubitOperatorString
], default:<factory>
) – Qubit operator kernel \(H\).
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.

bra_state:
GeneralAnsatz
¶
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
Union
[QubitOperator
,QubitOperatorString
]¶

ket_state:
GeneralAnsatz
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class OverlapSquared(bra_state, ket_state, kernel=<factory>)¶
Bases:
IOverlap
Represents the overlap squared of two states with a kernel operator.
\( \langle \Phi  P  \Psi \rangle ^2\)
Note
The kernel operator must be a single Pauli string.
 Parameters:
bra_state (
GeneralAnsatz
) – Bra state \(\Phi\rangle\).ket_state (
GeneralAnsatz
) – Ket state \(\Psi\rangle\).kernel (
Union
[QubitOperator
,QubitOperatorString
], default:<factory>
) – Qubit operator kernel \(H\).
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.

bra_state:
GeneralAnsatz
¶
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.

kernel:
Union
[QubitOperator
,QubitOperatorString
]¶

ket_state:
GeneralAnsatz
¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
inquanto.computables.primitive¶
Primitive objects for constructing quantum computable expressions.
 class ComputableFunction(func, *args)¶
Bases:
ComputableNode
[EvaluatedType
]Class representing a function applied to computable nodes in the expression tree.
 Parameters:
Example
>>> from inquanto.computables.primitive import ComputableInt >>> add = ComputableFunction(lambda x, y: x + y, ComputableInt(3), ComputableInt(4)) >>> result = add.evaluate() >>> result 7
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Recursively evaluates the expression tree and returns the computed result.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – Evaluator function passed to theevaluate()
methods of the child computable nodes recursively. Returns:
Union
[ComputableFunction
,TypeVar
(EvaluatedType
)] – The computed result of the expression tree.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ComputableInt(value)¶
Bases:
ComputableNode
[int
]Computable wrapper class for an int, mainly for demonstration purposes.
 Parameters:
value (
int
) – Integer value.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluates its value.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Any
]], default:None
) – Return type:
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ComputableList(iterable=(), /)¶
Bases:
list
,ComputableNode
[List
]Class representing a list of items of any types in the computable expression tree.
 Parameters:
iterable – An iterable which produces elements to initialize the list.
Example
>>> from inquanto.computables.primitive import ComputableInt >>> k_list = ComputableList([ComputableInt(1), ComputableInt(2), 3, "foo"]) >>> k_list [ComputableInt(value=1), ComputableInt(value=2), 3, 'foo'] >>> len(k_list) 4 >>> k_list.evaluate() [1, 2, 3, 'foo']
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 append(object, /)¶
Append object to the end of the list.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 clear()¶
Remove all items from list.
 copy()¶
Return a shallow copy of the list.
 count(value, /)¶
Return number of occurrences of value.
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluates each item in the list and returns the computed results as a list.
If an item is a computable, its
evaluate()
method is called. Otherwise, the item itself is returned. Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Any
]], default:None
) – Callable passed to each item’sevaluate()
method. Returns:
Union
[ComputableList
,List
] – The computed results of the items.
 extend(iterable, /)¶
Extend list by appending elements from the iterable.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
 insert(index, object, /)¶
Insert object before index.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 pop(index=1, /)¶
Remove and return item at index (default last).
Raises IndexError if list is empty or index is out of range.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 remove(value, /)¶
Remove first occurrence of value.
Raises ValueError if the value is not present.
 reverse()¶
Reverse IN PLACE.
 sort(*, key=None, reverse=False)¶
Sort the list in ascending order and return None.
The sort is inplace (i.e. the list itself is modified) and stable (i.e. the order of two equal elements is maintained).
If a key function is given, apply it once to each list item and sort them, ascending or descending, according to their function values.
The reverse flag can be set to sort in descending order.
 class ComputableNDArray(array_like: _SupportsArray[dtype[Any]]  _NestedSequence[_SupportsArray[dtype[Any]]]  bool  int  float  complex  str  bytes  _NestedSequence[bool  int  float  complex  str  bytes], *args: Any, **kwargs: Any)¶
Bases:
ndarray
,ComputableNode
[ndarray
[Any
,dtype
[_ScalarType_co
]]]Class representing a multidimensional array of items in a computable expression tree.
This class dresses numpy ndarrays with Computable methods. It can contain computable items as objects, allowing computations to be deferred. It provides an interface to seamlessly integrate within a computational framework that uses Computablebased structures.
The array can be of any dimension, and its constructor signature is the same as a numpy array with the dtype set to object if a computable element is used. Supports all mathematical operations.
 Parameters:
array_like – Initial data for the array. It can be a list, an already instantiated numpy array, or a list of Computable objects.
*args – Arguments passed to the numpy array constructor.
**kwargs – Key word arguments passed to the numpy array constructor, for example
dtype=object
Example
>>> from inquanto.computables.primitive import ComputableInt >>> qc_array = ComputableNDArray([ComputableInt(1), ComputableInt(2), ComputableInt(3), ComputableInt(4)], dtype=object) >>> qc_array.evaluate() array([1, 2, 3, 4], dtype=object)
>>> another_array = ComputableNDArray([ComputableInt(0), 1, ComputableInt(1), ComputableInt(0)]) >>> result = (qc_array + another_array) >>> result.evaluate() array([1, 3, 4, 4], dtype=object)
Note
The behavior of mathematical operations and functions on this class is determined by the behavior of the underlying numpy arrays. Computable items like
ComputableInt
will be evaluated when theevaluate()
method is called. T¶
View of the transposed array.
Same as
self.transpose()
.Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.T array([[1, 3], [2, 4]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.T array([1, 2, 3, 4])
See also
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 all(axis=None, out=None, keepdims=False, *, where=True)¶
Returns True if all elements evaluate to True.
Refer to numpy.all for full documentation.
See also
numpy.all
equivalent function
 any(axis=None, out=None, keepdims=False, *, where=True)¶
Returns True if any of the elements of a evaluate to True.
Refer to numpy.any for full documentation.
See also
numpy.any
equivalent function
 argmax(axis=None, out=None, *, keepdims=False)¶
Return indices of the maximum values along the given axis.
Refer to numpy.argmax for full documentation.
See also
numpy.argmax
equivalent function
 argmin(axis=None, out=None, *, keepdims=False)¶
Return indices of the minimum values along the given axis.
Refer to numpy.argmin for detailed documentation.
See also
numpy.argmin
equivalent function
 argpartition(kth, axis=1, kind='introselect', order=None)¶
Returns the indices that would partition this array.
Refer to numpy.argpartition for full documentation.
New in version 1.8.0.
See also
numpy.argpartition
equivalent function
 argsort(axis=1, kind=None, order=None)¶
Returns the indices that would sort this array.
Refer to numpy.argsort for full documentation.
See also
numpy.argsort
equivalent function
 astype(dtype, order='K', casting='unsafe', subok=True, copy=True)¶
Copy of the array, cast to a specified type.
 Parameters:
dtype (str or dtype) – Typecode or datatype to which the array is cast.
order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.
casting ({'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional) –
Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.
’no’ means the data types should not be cast at all.
’equiv’ means only byteorder changes are allowed.
’safe’ means only casts which can preserve values are allowed.
’same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
’unsafe’ means any data conversions may be done.
subok (bool, optional) – If True, then subclasses will be passedthrough (default), otherwise the returned array will be forced to be a baseclass array.
copy (bool, optional) – By default, astype always returns a newly allocated array. If this is set to false, and the dtype, order, and subok requirements are satisfied, the input array is returned instead of a copy.
 Returns:
arr_t (ndarray) – Unless copy is False and the other conditions for returning the input array are satisfied (see description for copy input parameter), arr_t is a new array of the same shape as the input array, with dtype, order given by dtype, order.
Notes
Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.
Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.
 Raises:
ComplexWarning – When casting from complex to float or int. To avoid this, one should use
a.real.astype(t)
.
Examples
>>> x = np.array([1, 2, 2.5]) >>> x array([1. , 2. , 2.5])
>>> x.astype(int) array([1, 2, 2])
 base¶
Base object if memory is from some other object.
Examples
The base of an array that owns its memory is None:
>>> x = np.array([1,2,3,4]) >>> x.base is None True
Slicing creates a view, whose memory is shared with x:
>>> y = x[2:] >>> y.base is x True
 byteswap(inplace=False)¶
Swap the bytes of the array elements
Toggle between lowendian and bigendian data representation by returning a byteswapped array, optionally swapped inplace. Arrays of bytestrings are not swapped. The real and imaginary parts of a complex number are swapped individually.
 Parameters:
inplace (bool, optional) – If
True
, swap bytes inplace, default isFalse
. Returns:
out (ndarray) – The byteswapped array. If inplace is
True
, this is a view to self.
Examples
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> list(map(hex, A)) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> list(map(hex, A)) ['0x100', '0x1', '0x3322']
Arrays of bytestrings are not swapped
>>> A = np.array([b'ceg', b'fac']) >>> A.byteswap() array([b'ceg', b'fac'], dtype='S3')
A.newbyteorder().byteswap()
produces an array with the same valuesbut different representation in memory
>>> A = np.array([1, 2, 3]) >>> A.view(np.uint8) array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], dtype=uint8) >>> A.newbyteorder().byteswap(inplace=True) array([1, 2, 3]) >>> A.view(np.uint8) array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3], dtype=uint8)
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 choose(choices, out=None, mode='raise')¶
Use an index array to construct a new array from a set of choices.
Refer to numpy.choose for full documentation.
See also
numpy.choose
equivalent function
 clip(min=None, max=None, out=None, **kwargs)¶
Return an array whose values are limited to
[min, max]
. One of max or min must be given.Refer to numpy.clip for full documentation.
See also
numpy.clip
equivalent function
 compress(condition, axis=None, out=None)¶
Return selected slices of this array along given axis.
Refer to numpy.compress for full documentation.
See also
numpy.compress
equivalent function
 conj()¶
Complexconjugate all elements.
Refer to numpy.conjugate for full documentation.
See also
numpy.conjugate
equivalent function
 conjugate()¶
Return the complex conjugate, elementwise.
Refer to numpy.conjugate for full documentation.
See also
numpy.conjugate
equivalent function
 copy(order='C')¶
Return a copy of the array.
 Parameters:
order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout of the copy. ‘C’ means Corder, ‘F’ means Forder, ‘A’ means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of a as closely as possible. (Note that this function and
numpy.copy()
are very similar but have different default values for their order= arguments, and this function always passes subclasses through.)
See also
numpy.copy
Similar function with different default behavior
numpy.copyto
Notes
This function is the preferred method for creating an array copy. The function
numpy.copy()
is similar, but it defaults to using order ‘K’, and will not pass subclasses through by default.Examples
>>> x = np.array([[1,2,3],[4,5,6]], order='F')
>>> y = x.copy()
>>> x.fill(0)
>>> x array([[0, 0, 0], [0, 0, 0]])
>>> y array([[1, 2, 3], [4, 5, 6]])
>>> y.flags['C_CONTIGUOUS'] True
 ctypes¶
An object to simplify the interaction of the array with the ctypes module.
This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.
 Parameters:
None –
 Returns:
c (Python object) – Possessing attributes data, shape, strides, etc.
See also
numpy.ctypeslib
Notes
Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):
 _ctypes.data
A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byteorder. The memory area may not even be writeable. The array flags and datatype of this array should be respected when passing this attribute to arbitrary Ccode to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as
self._array_interface_['data'][0]
.Note that unlike
data_as
, a reference will not be kept to the array: code likectypes.c_void_p((a + b).ctypes.data)
will result in a pointer to a deallocated array, and should be spelt(a + b).ctypes.data_as(ctypes.c_void_p)
 _ctypes.shape
A ctypes array of length self.ndim where the basetype is the Cinteger corresponding to
dtype('p')
on this platform (see ~numpy.ctypeslib.c_intp). This basetype could be ctypes.c_int, ctypes.c_long, or ctypes.c_longlong depending on the platform. The ctypes array contains the shape of the underlying array. Type:
(c_intp*self.ndim)
 _ctypes.strides
A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.
 Type:
(c_intp*self.ndim)
 _ctypes.data_as(obj)
Return the data pointer cast to a particular ctypes object. For example, calling
self._as_parameter_
is equivalent toself.data_as(ctypes.c_void_p)
. Perhaps you want to use the data as a pointer to a ctypes array of floatingpoint data:self.data_as(ctypes.POINTER(ctypes.c_double))
.The returned pointer will keep a reference to the array.
 _ctypes.shape_as(obj)
Return the shape tuple as an array of some other ctypes type. For example:
self.shape_as(ctypes.c_short)
.
 _ctypes.strides_as(obj)
Return the strides tuple as an array of some other ctypes type. For example:
self.strides_as(ctypes.c_longlong)
.
If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the
as_parameter
attribute which will return an integer equal to the data attribute.Examples
>>> import ctypes >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) >>> x array([[0, 1], [2, 3]], dtype=int32) >>> x.ctypes.data 31962608 # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents c_uint(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents c_ulong(4294967296) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 cumprod(axis=None, dtype=None, out=None)¶
Return the cumulative product of the elements along the given axis.
Refer to numpy.cumprod for full documentation.
See also
numpy.cumprod
equivalent function
 cumsum(axis=None, dtype=None, out=None)¶
Return the cumulative sum of the elements along the given axis.
Refer to numpy.cumsum for full documentation.
See also
numpy.cumsum
equivalent function
 data¶
Python buffer object pointing to the start of the array’s data.
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 diagonal(offset=0, axis1=0, axis2=1)¶
Return specified diagonals. In NumPy 1.9 the returned array is a readonly view instead of a copy as in previous NumPy versions. In a future version the readonly restriction will be removed.
Refer to
numpy.diagonal()
for full documentation.See also
numpy.diagonal
equivalent function
 dot()¶
 dtype¶
Datatype of the array’s elements.
Warning
Setting
arr.dtype
is discouraged and may be deprecated in the future. Setting will replace thedtype
without modifying the memory (see also ndarray.view and ndarray.astype). Parameters:
None –
 Returns:
d (numpy dtype object)
See also
ndarray.astype
Cast the values contained in the array to a new datatype.
ndarray.view
Create a view of the same data but a different datatype.
numpy.dtype
Examples
>>> x array([[0, 1], [2, 3]]) >>> x.dtype dtype('int32') >>> type(x.dtype) <type 'numpy.dtype'>
 dump(file)¶
Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.
 Parameters:
file (str or Path) –
A string naming the dump file.
Changed in version 1.17.0: pathlib.Path objects are now accepted.
 dumps()¶
Returns the pickle of the array as a string. pickle.loads will convert the string back to an array.
 Parameters:
None –
 evaluate(evaluator=None)¶
Evaluates each item in the array and returns the computed results as an array.
If an item is a computable, its
evaluate()
method is called. Otherwise, the item itself is returned. Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Any
]], default:None
) – Callable passed to each item’sevaluate()
method. Returns:
Union
[ComputableNDArray
,ndarray
[Any
,dtype
[TypeVar
(_ScalarType_co
, bound=generic
, covariant=True)]]] – The computed results of the items.
 fill(value)¶
Fill the array with a scalar value.
 Parameters:
value (scalar) – All elements of a will be assigned this value.
Examples
>>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([1., 1.])
Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:
>>> a = np.array([None, None], dtype=object) >>> a[0] = np.array(3) >>> a array([array(3), None], dtype=object) >>> a.fill(np.array(3)) >>> a array([array(3), array(3)], dtype=object)
Where other forms of assignments will unpack the array being assigned:
>>> a[...] = np.array(3) >>> a array([3, 3], dtype=object)
 flags¶
Information about the memory layout of the array.
 C_CONTIGUOUS(C)¶
The data is in a single, Cstyle contiguous segment.
 F_CONTIGUOUS(F)¶
The data is in a single, Fortranstyle contiguous segment.
 OWNDATA(O)¶
The array owns the memory it uses or borrows it from another object.
 WRITEABLE(W)¶
The data area can be written to. Setting this to False locks the data, making it readonly. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a nonwriteable array raises a RuntimeError exception.
 ALIGNED(A)¶
The data and all elements are aligned appropriately for the hardware.
 WRITEBACKIFCOPY(X)¶
This array is a copy of some other array. The CAPI function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.
 FNC¶
F_CONTIGUOUS and not C_CONTIGUOUS.
 FORC¶
F_CONTIGUOUS or C_CONTIGUOUS (onesegment test).
 BEHAVED(B)¶
ALIGNED and WRITEABLE.
 CARRAY(CA)¶
BEHAVED and C_CONTIGUOUS.
 FARRAY(FA)¶
BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
Notes
The flags object can be accessed dictionarylike (as in
a.flags['WRITEABLE']
), or by using lowercased attribute names (as ina.flags.writeable
). Short flag names are only supported in dictionary access.Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling ndarray.setflags.
The array flags cannot be set arbitrarily:
WRITEBACKIFCOPY can only be set
False
.ALIGNED can only be set
True
if the data is truly aligned.WRITEABLE can only be set
True
if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.
Arrays can be both Cstyle and Fortranstyle contiguous simultaneously. This is clear for 1dimensional arrays, but can also be true for higher dimensional arrays.
Even for contiguous arrays a stride for a given dimension
arr.strides[dim]
may be arbitrary ifarr.shape[dim] == 1
or the array has no elements. It does not generally hold thatself.strides[1] == self.itemsize
for Cstyle contiguous arrays orself.strides[0] == self.itemsize
for Fortranstyle contiguous arrays is true.
 flat¶
A 1D iterator over the array.
This is a numpy.flatiter instance, which acts similarly to, but is not a subclass of, Python’s builtin iterator object.
Examples
>>> x = np.arange(1, 7).reshape(2, 3) >>> x array([[1, 2, 3], [4, 5, 6]]) >>> x.flat[3] 4 >>> x.T array([[1, 4], [2, 5], [3, 6]]) >>> x.T.flat[3] 5 >>> type(x.flat) <class 'numpy.flatiter'>
An assignment example:
>>> x.flat = 3; x array([[3, 3, 3], [3, 3, 3]]) >>> x.flat[[1,4]] = 1; x array([[3, 1, 3], [3, 1, 3]])
 flatten(order='C')¶
Return a copy of the array collapsed into one dimension.
 Parameters:
order ({'C', 'F', 'A', 'K'}, optional) – ‘C’ means to flatten in rowmajor (Cstyle) order. ‘F’ means to flatten in columnmajor (Fortran style) order. ‘A’ means to flatten in columnmajor order if a is Fortran contiguous in memory, rowmajor order otherwise. ‘K’ means to flatten a in the order the elements occur in memory. The default is ‘C’.
 Returns:
y (ndarray) – A copy of the input array, flattened to one dimension.
Examples
>>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 getfield(dtype, offset=0)¶
Returns a field of the given array as a certain type.
A field is a view of the array data with a given datatype. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16byte elements. If taking a view with a 32bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.
 Parameters:
Examples
>>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[1.+1.j, 0.+0.j], [0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[1., 0.], [0., 2.]])
By choosing an offset of 8 bytes we can select the complex part of the array for our view:
>>> x.getfield(np.float64, offset=8) array([[1., 0.], [0., 4.]])
 imag¶
The imaginary part of the array.
Examples
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.imag array([ 0. , 0.70710678]) >>> x.imag.dtype dtype('float64')
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 item(*args)¶
Copy an element of an array to a standard Python scalar and return it.
 Parameters:
*args (Arguments (variable number and type)) –
none: in this case, the method only works for arrays with one element (a.size == 1), which element is copied into a standard Python scalar object and returned.
int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.
tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an ndindex into the array.
 Returns:
z (Standard Python scalar object) – A copy of the specified element of the array as a suitable Python scalar
Notes
When the data type of a is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.
item is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.
Examples
>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.item(3) 1 >>> x.item(7) 0 >>> x.item((0, 1)) 2 >>> x.item((2, 2)) 1
 itemset(*args)¶
Insert scalar into an array (scalar is cast to array’s dtype, if possible)
There must be at least 1 argument, and define the last argument as item. Then,
a.itemset(*args)
is equivalent to but faster thana[args] = item
. The item should be a scalar value and args must select a single item in the array a. Parameters:
*args (Arguments) – If one argument: a scalar, only used in case a is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.
Notes
Compared to indexing syntax, itemset provides some speed increase for placing a scalar into a particular location in an ndarray, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using itemset (and item) inside a loop, be sure to assign the methods to a local variable to avoid the attribute lookup at each loop iteration.
Examples
>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[2, 2, 6], [1, 0, 6], [1, 0, 9]])
 itemsize¶
Length of one array element in bytes.
Examples
>>> x = np.array([1,2,3], dtype=np.float64) >>> x.itemsize 8 >>> x = np.array([1,2,3], dtype=np.complex128) >>> x.itemsize 16
 max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶
Return the maximum along a given axis.
Refer to numpy.amax for full documentation.
See also
numpy.amax
equivalent function
 mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)¶
Returns the average of the array elements along given axis.
Refer to numpy.mean for full documentation.
See also
numpy.mean
equivalent function
 min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶
Return the minimum along a given axis.
Refer to numpy.amin for full documentation.
See also
numpy.amin
equivalent function
 nbytes¶
Total bytes consumed by the elements of the array.
Notes
Does not include memory consumed by nonelement attributes of the array object.
See also
sys.getsizeof
Memory consumed by the object itself without parents in case view. This does include memory consumed by nonelement attributes.
Examples
>>> x = np.zeros((3,5,2), dtype=np.complex128) >>> x.nbytes 480 >>> np.prod(x.shape) * x.itemsize 480
 ndim¶
Number of array dimensions.
Examples
>>> x = np.array([1, 2, 3]) >>> x.ndim 1 >>> y = np.zeros((2, 3, 4)) >>> y.ndim 3
 newbyteorder(new_order='S', /)¶
Return the array with the same data viewed with a different byte order.
Equivalent to:
arr.view(arr.dtype.newbytorder(new_order))
Changes are also made in all fields and subarrays of the array data type.
 Parameters:
new_order (string, optional) –
Byte order to force; a value from the byte order specifications below. new_order codes can be any of:
’S’  swap dtype from current to opposite endian
{‘<’, ‘little’}  little endian
{‘>’, ‘big’}  big endian
{‘=’, ‘native’}  native order, equivalent to sys.byteorder
{‘’, ‘I’}  ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order.
 Returns:
new_arr (array) – New array object with the dtype reflecting given change to the byte order.
 nonzero()¶
Return the indices of the elements that are nonzero.
Refer to numpy.nonzero for full documentation.
See also
numpy.nonzero
equivalent function
 partition(kth, axis=1, kind='introselect', order=None)¶
Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.
New in version 1.8.0.
 Parameters:
kth (int or sequence of ints) –
Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.
Deprecated since version 1.22.0: Passing booleans as index is deprecated.
axis (int, optional) – Axis along which to sort. Default is 1, which means sort along the last axis.
kind ({'introselect'}, optional) – Selection algorithm. Default is ‘introselect’.
order (str or list of str, optional) – When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
See also
numpy.partition
Return a partitioned copy of an array.
argpartition
Indirect partition.
sort
Full sort.
Notes
See
np.partition
for notes on the different algorithms.Examples
>>> a = np.array([3, 4, 2, 1]) >>> a.partition(3) >>> a array([2, 1, 3, 4])
>>> a.partition((1, 3)) >>> a array([1, 2, 3, 4])
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)¶
Return the product of the array elements over the given axis
Refer to numpy.prod for full documentation.
See also
numpy.prod
equivalent function
 ptp(axis=None, out=None, keepdims=False)¶
Peak to peak (maximum  minimum) value along a given axis.
Refer to numpy.ptp for full documentation.
See also
numpy.ptp
equivalent function
 put(indices, values, mode='raise')¶
Set
a.flat[n] = values[n]
for all n in indices.Refer to numpy.put for full documentation.
See also
numpy.put
equivalent function
 ravel([order])¶
Return a flattened array.
Refer to numpy.ravel for full documentation.
See also
numpy.ravel
equivalent function
ndarray.flat
a flat iterator on the array.
 real¶
The real part of the array.
Examples
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.real array([ 1. , 0.70710678]) >>> x.real.dtype dtype('float64')
See also
numpy.real
equivalent function
 repeat(repeats, axis=None)¶
Repeat elements of an array.
Refer to numpy.repeat for full documentation.
See also
numpy.repeat
equivalent function
 reshape(shape, order='C')¶
Returns an array containing the same data with a new shape.
Refer to numpy.reshape for full documentation.
See also
numpy.reshape
equivalent function
Notes
Unlike the free function numpy.reshape, this method on ndarray allows the elements of the shape parameter to be passed in as separate arguments. For example,
a.reshape(10, 11)
is equivalent toa.reshape((10, 11))
.
 resize(new_shape, refcheck=True)¶
Change shape and size of array inplace.
 Parameters:
new_shape (tuple of ints, or n ints) – Shape of resized array.
refcheck (bool, optional) – If False, reference count will not be checked. Default is True.
 Returns:
None
 Raises:
ValueError – If a does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.
SystemError – If the order keyword argument is specified. This behaviour is a bug in NumPy.
See also
resize
Return a new array with the specified shape.
Notes
This reallocates space for the data area if necessary.
Only contiguous arrays (data elements consecutive in memory) can be resized.
The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set refcheck to False.
Examples
Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:
>>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]])
>>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]])
Enlarging an array: as above, but missing entries are filled with zeros:
>>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]])
Referencing an array prevents resizing…
>>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that references or is referenced ...
Unless refcheck is False:
>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])
 round(decimals=0, out=None)¶
Return a with each element rounded to the given number of decimals.
Refer to numpy.around for full documentation.
See also
numpy.around
equivalent function
 searchsorted(v, side='left', sorter=None)¶
Find indices where elements of v should be inserted in a to maintain order.
For full documentation, see numpy.searchsorted
See also
numpy.searchsorted
equivalent function
 setfield(val, dtype, offset=0)¶
Put a value into a specified place in a field defined by a datatype.
Place val into a’s field defined by dtype and beginning offset bytes into the field.
 Parameters:
 Returns:
None
See also
Examples
>>> x = np.eye(3) >>> x.getfield(np.float64) array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]], dtype=int32) >>> x array([[1.0e+000, 1.5e323, 1.5e323], [1.5e323, 1.0e+000, 1.5e323], [1.5e323, 1.5e323, 1.0e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])
 setflags(write=None, align=None, uic=None)¶
Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
These Booleanvalued flags affect how numpy interprets the memory area used by a (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)
 Parameters:
Notes
Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
WRITEABLE (W) the data area can be written to;
ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);
WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the CAPI function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.
All flags can be accessed using the single (upper case) letter as well as the full name.
Examples
>>> y = np.array([[3, 1, 7], ... [2, 0, 0], ... [8, 5, 9]]) >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: cannot set WRITEBACKIFCOPY flag to True
 shape¶
Tuple of array dimensions.
The shape property is usually used to get the current shape of an array, but may also be used to reshape the array inplace by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be 1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array inplace will fail if a copy is required.
Warning
Setting
arr.shape
is discouraged and may be deprecated in the future. Using ndarray.reshape is the preferred approach.Examples
>>> x = np.array([1, 2, 3, 4]) >>> x.shape (4,) >>> y = np.zeros((2, 3, 4)) >>> y.shape (2, 3, 4) >>> y.shape = (3, 8) >>> y array([[ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.]]) >>> y.shape = (3, 6) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: total size of new array must be unchanged >>> np.zeros((4,2))[::2].shape = (1,) Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: Incompatible shape for inplace modification. Use `.reshape()` to make a copy with the desired shape.
See also
numpy.shape
Equivalent getter function.
numpy.reshape
Function similar to setting
shape
.ndarray.reshape
Method similar to setting
shape
.
 size¶
Number of elements in the array.
Equal to
np.prod(a.shape)
, i.e., the product of the array’s dimensions.Notes
a.size returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested
np.prod(a.shape)
, which returns an instance ofnp.int_
), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.Examples
>>> x = np.zeros((3, 5, 2), dtype=np.complex128) >>> x.size 30 >>> np.prod(x.shape) 30
 sort(axis=1, kind=None, order=None)¶
Sort an array inplace. Refer to numpy.sort for full documentation.
 Parameters:
axis (int, optional) – Axis along which to sort. Default is 1, which means sort along the last axis.
kind ({'quicksort', 'mergesort', 'heapsort', 'stable'}, optional) –
Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.
Changed in version 1.15.0: The ‘stable’ option was added.
order (str or list of str, optional) – When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
See also
numpy.sort
Return a sorted copy of an array.
numpy.argsort
Indirect sort.
numpy.lexsort
Indirect stable sort on multiple keys.
numpy.searchsorted
Find elements in sorted array.
numpy.partition
Partial sort.
Notes
See numpy.sort for notes on the different sorting algorithms.
Examples
>>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]])
Use the order keyword to specify a field to use when sorting a structured array:
>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([(b'c', 1), (b'a', 2)], dtype=[('x', 'S1'), ('y', '<i8')])
 squeeze(axis=None)¶
Remove axes of length one from a.
Refer to numpy.squeeze for full documentation.
See also
numpy.squeeze
equivalent function
 std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
Returns the standard deviation of the array elements along given axis.
Refer to numpy.std for full documentation.
See also
numpy.std
equivalent function
 strides¶
Tuple of bytes to step in each dimension when traversing an array.
The byte offset of element
(i[0], i[1], ..., i[n])
in an array a is:offset = sum(np.array(i) * a.strides)
A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.
Warning
Setting
arr.strides
is discouraged and may be deprecated in the future. numpy.lib.stride_tricks.as_strided should be preferred to create a new view of the same data in a safer way.Notes
Imagine an array of 32bit integers (each 4 bytes):
x = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array x will be
(20, 4)
.See also
numpy.lib.stride_tricks.as_strided
Examples
>>> y = np.reshape(np.arange(2*3*4), (2,3,4)) >>> y array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y.strides (48, 16, 4) >>> y[1,1,1] 17 >>> offset=sum(y.strides * np.array((1,1,1))) >>> offset/y.itemsize 17
>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) >>> x.strides (32, 4, 224, 1344) >>> i = np.array([3,5,2,2]) >>> offset = sum(i * x.strides) >>> x[3,5,2,2] 813 >>> offset / x.itemsize 813
 sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)¶
Return the sum of the array elements over the given axis.
Refer to numpy.sum for full documentation.
See also
numpy.sum
equivalent function
 swapaxes(axis1, axis2)¶
Return a view of the array with axis1 and axis2 interchanged.
Refer to numpy.swapaxes for full documentation.
See also
numpy.swapaxes
equivalent function
 take(indices, axis=None, out=None, mode='raise')¶
Return an array formed from the elements of a at the given indices.
Refer to numpy.take for full documentation.
See also
numpy.take
equivalent function
 tobytes(order='C')¶
Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in Corder by default. This behavior is controlled by the
order
parameter.New in version 1.9.0.
 Parameters:
order ({'C', 'F', 'A'}, optional) – Controls the memory layout of the bytes object. ‘C’ means Corder, ‘F’ means Forder, ‘A’ (short for Any) means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.
 Returns:
s (bytes) – Python bytes exhibiting a copy of a’s raw data.
See also
frombuffer
Inverse of this operation, construct a 1dimensional array from Python bytes.
Examples
>>> x = np.array([[0, 1], [2, 3]], dtype='<u2') >>> x.tobytes() b'\x00\x00\x01\x00\x02\x00\x03\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x02\x00\x01\x00\x03\x00'
 tofile(fid, sep='', format='%s')¶
Write array to a file as text or binary (default).
Data is always written in ‘C’ order, independent of the order of a. The data produced by this method can be recovered using the function fromfile().
 Parameters:
fid (file or str or Path) –
An open file object, or a string containing a filename.
Changed in version 1.17.0: pathlib.Path objects are now accepted.
sep (str) – Separator between array items for text output. If “” (empty), a binary file is written, equivalent to
file.write(a.tobytes())
.format (str) – Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.
Notes
This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.
When fid is a file object, array contents are directly written to the file, bypassing the file object’s
write
method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or filelike objects that do not supportfileno()
(e.g., BytesIO).
 tolist()¶
Return the array as an
a.ndim
levels deep nested list of Python scalars.Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the ~numpy.ndarray.item function.
If
a.ndim
is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar. Parameters:
none –
 Returns:
y (object, or list of object, or list of list of object, or …) – The possibly nested list of array elements.
Notes
The array may be recreated via
a = np.array(a.tolist())
, although this may sometimes lose precision.Examples
For a 1D array,
a.tolist()
is almost the same aslist(a)
, except thattolist
changes numpy scalars to Python scalars:>>> a = np.uint32([1, 2]) >>> a_list = list(a) >>> a_list [1, 2] >>> type(a_list[0]) <class 'numpy.uint32'> >>> a_tolist = a.tolist() >>> a_tolist [1, 2] >>> type(a_tolist[0]) <class 'int'>
Additionally, for a 2D array,
tolist
applies recursively:>>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
The base case for this recursion is a 0D array:
>>> a = np.array(1) >>> list(a) Traceback (most recent call last): ... TypeError: iteration over a 0d array >>> a.tolist() 1
 tostring(order='C')¶
A compatibility alias for tobytes, with exactly the same behavior.
Despite its name, it returns bytes not strs.
Deprecated since version 1.19.0.
 trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)¶
Return the sum along diagonals of the array.
Refer to numpy.trace for full documentation.
See also
numpy.trace
equivalent function
 transpose(*axes)¶
Returns a view of the array with axes transposed.
Refer to numpy.transpose for full documentation.
 Parameters:
axes (None, tuple of ints, or n ints) –
None or no argument: reverses the order of the axes.
tuple of ints: i in the jth place in the tuple means that the array’s ith axis becomes the transposed array’s jth axis.
n ints: same as an ntuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form).
 Returns:
p (ndarray) – View of the array with its axes suitably permuted.
See also
transpose
Equivalent function.
ndarray.T
Array property returning the array transposed.
ndarray.reshape
Give a new shape to an array without changing its data.
Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.transpose() array([1, 2, 3, 4])
 var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
Returns the variance of the array elements, along given axis.
Refer to numpy.var for full documentation.
See also
numpy.var
equivalent function
 view([dtype][, type])¶
New view of array with the same data.
Note
Passing None for
dtype
is different from omitting the parameter, since the former invokesdtype(None)
which is an alias fordtype('float_')
. Parameters:
dtype (datatype or ndarray subclass, optional) – Datatype descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same datatype as a. This argument can also be specified as an ndarray subclass, which then specifies the type of the returned object (this is equivalent to setting the
type
parameter).type (Python type, optional) – Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.
Notes
a.view()
is used two different ways:a.view(some_dtype)
ora.view(dtype=some_dtype)
constructs a view of the array’s memory with a different datatype. This can cause a reinterpretation of the bytes of memory.a.view(ndarray_subclass)
ora.view(type=ndarray_subclass)
just returns an instance of ndarray_subclass that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.For
a.view(some_dtype)
, ifsome_dtype
has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis ofa
must be contiguous. This axis will be resized in the result.Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be Ccontiguous.
Examples
>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
Viewing array data using a different type and dtype:
>>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print(type(y)) <class 'numpy.matrix'>
Creating a view on a structured array so it can be used in calculations
>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([2., 3.])
Making changes to the view changes the underlying array
>>> xv[0,1] = 20 >>> x array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1, 3], dtype=int8)
Views share data:
>>> x[0] = (9, 10) >>> z[0] (9, 10)
Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortranordering, etc.:
>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16) >>> y = x[:, ::2] >>> y array([[1, 3], [4, 6]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): ... ValueError: To change to a dtype of a different size, the last axis must be contiguous >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 3)], [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not Ccontiguous:
>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4) >>> x.transpose(1, 0, 2).view(np.int16) array([[[ 256, 770], [3340, 3854]], [[1284, 1798], [4368, 4882]], [[2312, 2826], [5396, 5910]]], dtype=int16)
 class ComputableNode¶
Bases:
Evaluatable
[EvaluatedType
]Base class representing a computable node in an expression tree.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ComputableSingleChild¶
Bases:
ComputableNode
[EvaluatedType
]Computable class which has a single child.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(TQCOne
, bound= ComputableSingleChild),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ComputableTuple(*items: Any)¶
Bases:
tuple
,ComputableNode
[Tuple
]Class representing a tuple of items of any types in the computable expression tree.
 Parameters:
*items – One or more items, which can be of any type.
Example
>>> from inquanto.computables.primitive import ComputableInt >>> k_tuple = ComputableTuple(ComputableInt(1), ComputableInt(2), 3, "foo") >>> k_tuple (ComputableInt(value=1), ComputableInt(value=2), 3, 'foo') >>> len(k_tuple) 4 >>> k_tuple.evaluate() (1, 2, 3, 'foo')
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 evaluate(evaluator=None)¶
Evaluates each item in the tuple and returns the computed results as a tuple.
If an item is a computable, its
evaluate()
method is called. Otherwise, the item itself is returned. Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Any
]], default:None
) – Callable passed to each item’sevaluate()
method. Returns:
Union
[ComputableTuple
,Tuple
] – The computed results of the items.
 class Evaluatable¶
Bases:
Generic
[EvaluatedType
]Base class for classes that have
evaluate()
methods. default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(EvaluatableType
, bound= Evaluatable),TypeVar
(EvaluatedType
)] – The computed result.
inquanto.computables.composite¶
Submodule for composite quantum computable expressions. Composed of atomic computables.
 class CommutatorComputable(state, operator_left, operator_right)¶
Bases:
ComputableSingleChild
[complex
]Computable expression to calculate the expectation value of commutator between two qubit operators.
Represents the expression \(\langle \Psi  [A, B]  \Psi\rangle\).
 Parameters:
state (
GeneralAnsatz
) – Trial state \(\Psi\rangle\).operator_left (
QubitOperator
) – Lefthand operator \(A\).operator_right (
QubitOperator
) – Righthand operator \(B\).
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(TQCOne
, bound= ComputableSingleChild),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ExpectationValueSumComputable(states, kernels)¶
Bases:
ComputableSingleChild
[float
]Computable expression to calculate the sum of expectation values with different states and hermitian kernels.
Represents the expression \(\sum_i \langle \psi_i  A  \psi_i \rangle\) or \(\sum_i \langle \psi_i  A_i  \psi_i \rangle\).
 Parameters:
states (
Sequence
[GeneralAnsatz
]) – List of states.kernels (
Union
[QubitOperator
,Sequence
[QubitOperator
]]) – Hermitian kernel, or list of hermitian kernels. If a list is provided,kernel[i]
corresponds tostates[i]
.
 Raises:
ValueError – If a list of
kernels
is provided which is not the same length asstates
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(TQCOne
, bound= ComputableSingleChild),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class HoleGFComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())¶
Bases:
ComputableSingleChild
[Expr
]Computable expression for the Manybody hole Green’s function.
Internally it measures the moments to compute the Lanczos coefficients, and it will be used to evaluate the Green’s function matrix elements.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.krylov (
int
) – Dimension of the Krylov space.left (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the left.right (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of theleft
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Expr
– The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class KrylovSubspace(moments)¶
Bases:
object
Helper class for Lanczos coefficients.
Calculates \(\alpha_n\) and \(\beta_n\) coefficients for the Krylovspace from a list of moments. If the number of moments is \(2*n1\) then the Krylovspace has a dimension \(n\).
 Parameters:
moments (
Union
[List
[float
],List
[Expr
]]) – List of moments as[<>, <H>, <H^2>, ..., <H^(2*n1)>]
.
 alpha_f(n)¶
Recursively computes nth alpha Lanczos coefficient.
 beta_f(n)¶
Recursively computes nth beta Lanczos coefficient.
 construct_symbolic_recursive_gf(z=Symbol('z'), factor=1.0, shift=0.0, tolerance=1e8)¶
Generate an expression for the Green’s function with the recursive formulae.
 Parameters:
z (
Union
[float
,Expr
], default:Symbol("z")
) – Symbol z is the complex energy.factor (
float
, default:1.0
) – This is +1 or 1, for particle or hole, respectively.shift (
Union
[float
,Expr
], default:0.0
) – The ground energy shift.tolerance (
float
, default:1e8
) – Stop the recursion if bn is smaller than the tolerance.
 Returns:
Union
[float
,complex
,Expr
] – Symbolic expression for G(z) approximation.
 construct_symbolic_recursive_gf_h(z=Symbol('z'), e0=Symbol('e0'), eta=Symbol('eta'))¶
Expression for the hole Green’s function with the recursive formulae.
Note: Equivalent to
construct_symbolic_recursive_gf(z, 1, e0 + I * eta)
.
 construct_symbolic_recursive_gf_p(z=Symbol('z'), e0=Symbol('e0'), eta=Symbol('eta'))¶
Expression for the particle Green’s function with the recursive formulae.
Note: Equivalent to
construct_symbolic_recursive_gf(z, +1, e0 + I * eta)
.
 construct_symbolic_recursive_lanczos_gf00(z=Symbol('z'))¶
Expression for the Greens function with the recursive formulae.
Note: Equivalent to
construct_symbolic_recursive_gf(z, +1, 0)
.
 construct_tridiagonal_representation()¶
Constructs the tridiagonal representation of the Hamiltonian.
 eigenvalues()¶
Eigenvalues of the Lanczos matrix.
 factors()¶
Calculates the Lanczos coefficients.
 class KrylovSubspaceComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())¶
Bases:
ComputableSingleChild
[KrylovSubspace
]Computable expression for
KrylovSubspace
moments.Based on arXiv:2009.13140 <https://arxiv.org/pdf/2009.13140.pdf>.
Indirectly measures the moments to compute the Lanczos coefficients \(\alpha_n\) and \(\beta_n\) of the Krylovspace.
More precisely, internally it will measure \(\langle\Psi(\theta)  L * H^n * R \Psi(\theta)\rangle\) where H is a hermitian operator, \(L\), \(R = L^{\dagger}\) are left and right operators, usually identities.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.krylov (
int
) – Dimension of the Krylov space.left (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the left.right (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of theleft
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
KrylovSubspace
– The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class LanczosCoefficientsComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())¶
Bases:
ComputableSingleChild
[Tuple
[List
[float
],List
[float
]]]Computable expression for the Lanczos coefficients.
Internally it measures the moments to compute the Lanczos coefficients \(\alpha_n\) and \(\beta_n\) of the Krylovspace.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.krylov (
int
) – Dimension of the Krylov space.left (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the left.right (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of theleft
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class LanczosMatrixComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())¶
Bases:
ComputableSingleChild
[ndarray
[Any
,dtype
[_ScalarType_co
]]]Computable expression for the tridiagonal Lanczos matrix.
Internally it measures the moments to compute the tridiagonal Lanczos matrix with coefficients \(\alpha_n\) and \(\beta_n\) of the Krylovspace.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.krylov (
int
) – Dimension of the Krylov space.left (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the left.right (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of theleft
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
ndarray
[Any
,dtype
[TypeVar
(_ScalarType_co
, bound=generic
, covariant=True)]] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ManyBodyGFComputable(fermion_space, ground_state, hamiltonian, krylov, encoding=QubitMappingJordanWigner(), ground_state_energy=None, eta=0)¶
Bases:
ComputableSingleChild
[MutableDenseMatrix
]Computable expression for the 1particle ManyBody Green’s function matrix, in a basis of spin orbitals.
 Parameters:
fermion_space (
FermionSpace
) – Fermion occupation space described by this Green’s function.ground_state (
GeneralAnsatz
) – Ground state.hamiltonian (
Union
[QubitOperator
,FermionOperator
]) – Hamiltonian of the system.krylov (
int
) – Dimension of the Krylov space.encoding (
QubitMapping
, default:QubitMappingJordanWigner()
) – Fermion to qubit mapping.ground_state_energy (
Optional
[float
], default:None
) – Ground state energy.eta (
Union
[Symbol
,float
], default:0
) – Infinitesimal number for the manybody Green’s function.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 default_evaluate_as_function(parameters=None)¶
Evaluates to a function with the default protocol.
Evaluates the Green’s function matrix with the default protocol and simulator and constructs a function from complex energy to a numpy matrix.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
MutableDenseMatrix
– The computed result.
 evaluate_as_function(evaluator=None)¶
Evaluates to a function.
Evaluates the GF matrix and constructs a function from complex energy to a numpy matrix.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class NonOrthogonalMatricesComputable(hermitian_operator, states)¶
Bases:
ComputableNode
Computable expression representing NO (Non Orthogonal) matrices.
Measure matrix elements of a matrix \(H\) and overlap matrix \(S\) in the generalised eigenvalue equation \(HC = eSC\). The \(H\) matrix is the matrix representation of a Hermitian operator, typically the Hamiltonian, in the subspace spanned by a list of states, and \(S\) is the overlap matrix of the states.
Both, \(H\) and \(S\) matrices are represented with
OverlapMatrixComputable
internally.Based on arxiv.org/abs/2205.09039.
 Parameters:
hermitian_operator (
QubitOperator
) – A Hermitian operator, typically a Hamiltonian, to be expanded in the subspace.states (
List
[GeneralAnsatz
]) – Ansatz states used to span the subspace.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[NonOrthogonalMatricesComputable
,Tuple
[ndarray
[Any
,dtype
[TypeVar
(_ScalarType_co
, bound=generic
, covariant=True)]],ndarray
[Any
,dtype
[TypeVar
(_ScalarType_co
, bound=generic
, covariant=True)]]]] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class OverlapMatrixComputable(states, kernel=QubitOperator.identity())¶
Bases:
ComputableNode
Computable expression representing an overlap matrix.
The general overlap matrix defined as \(S_{ij} = \langle\Psi_i\hat{O}\Psi_j\rangle\) where \(\hat{O}\) kernel is a Hermitian qubit operator and \(\Psi_i\rangle\) are normalised states as ansatzes.
The diagonal elements of the overlap matrix are represented with
ExpectationValue
computables if the kernel is not identity, while the offdiagonal elements are represented withOverlap
computables. Since the overlap matrix is a Hermitian matrix, the lower triangular part is excluded from any subsequent measurements or simulation workflow and on evaluation it is computed from the upper triangular part. If the kernel is identity, the diagonal elements are set to 1 and the expectation values are not included into any measurements or simulation workflow. Parameters:
states (
List
[GeneralAnsatz
]) – Ansatz states used to span the subspace.kernel (
QubitOperator
, default:QubitOperator.identity()
) – An optional Hermitian operator, by default it is identity.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[OverlapMatrixComputable
,ndarray
[Any
,dtype
[TypeVar
(_ScalarType_co
, bound=generic
, covariant=True)]]] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class PDM1234RealComputable(space, ansatz, encoding, symmetry_operators, cas_elec, cas_orbs, cu4=True, taperer=None)¶
Bases:
ComputableSingleChild
[Tuple
[ndarray
[Any
,dtype
[_ScalarType_co
]], …]]Computable expressions for 1,2,3PDMs of a given state, defined by ansatz and parameters.
Represents the PreDensity Matrix (PDM) according to doi.org/10.1063/5.0051211.
 Parameters:
space (
FermionSpace
) – Fermion occupation space spanned by this RDM.ansatz (
GeneralAnsatz
) – Ansatz state with respect to which expectation values are computed.encoding (
QubitMapping
) – Fermion to qubit mapping.symmetry_operators (
List
[SymmetryOperatorPauli
]) – Z2 symmetries of the Hamiltonian.cas_elec (
int
) – Number of active electrons.cas_orbs (
int
) – Number of active orbitals.cu4 (
bool
, default:True
) – If True (default), the 4PDM is estimated via the cumulant expansion approximation, otherwise it is measured.taperer (
Optional
[TapererZ2
], default:None
) – TapererZ2 initialized with the Hamiltonian, or None if tapering is not used.
Note
1,2,3,4PDMs are returned as a list of arrays, in PySCFstyle ordering (<p^r^sq>)
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(*args, **kwargs)¶
Evaluate this object using the provided evaluator function.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class ParticleGFComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())¶
Bases:
ComputableSingleChild
[Expr
]Computable expression for the Manybody particle Green’s function.
Internally it measures the moments to compute the Lanczos coefficients, and it will be used to evaluate the Green’s function matrix elements.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.krylov (
int
) – Dimension of the Krylov space.left (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the left.right (
QubitOperator
, default:QubitOperator.identity()
) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of theleft
.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Expr
– The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class QCM4Computable(state, kernel)¶
Bases:
ComputableSingleChild
[KrylovSubspace
]Computable expression for infimum approximation quantum computed moments up to order of 4.
Based on arXiv:2311.02533 <https://arxiv.org/pdf/2311.02533>.
 Parameters:
state (
GeneralAnsatz
) –kernel (
QubitOperator
) –
 __init__(state, kernel)¶
Quantum computed moment computable to approximate the lowest eigenvalue of the kernel.
 Parameters:
state (
GeneralAnsatz
) – Initial ansatz state.kernel (
QubitOperator
) – Hermitian operator kernel.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(evaluator=None)¶
Evaluate this object using the provided evaluator function.
 Parameters:
evaluator (
Optional
[Callable
[[Evaluatable
],Union
[Evaluatable
,Any
]]], default:None
) – A callable evaluator that is called on the instance. Returns:
Union
[TypeVar
(TQCOne
, bound= ComputableSingleChild),TypeVar
(EvaluatedType
)] – The computed result.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class QSEMatricesComputable(state, hermitian_operator, expansion_operators)¶
Bases:
ComputableNode
Computable expression representing QSE (quantum subspace expansion) matrices.
Measure matrix elements of a matrix \(H\) and overlap matrix \(S\) in the generalised eigenvalue equation \(HC = eSC\). The \(H\) matrix is the matrix representation of a Hermitian operator, typically the Hamiltonian, in the subspace spanned by the excitation operators, and \(S\) is the overlap matrix of the subspace generating states. QSE aims to obtain a description of lowlying excited states described as an expansion of excitation operators acting on the effective groundstate obtained from a variational calculation.
Based on arXiv:1603.05681.
 Parameters:
state (
GeneralAnsatz
) – Ansatz used to represent the ground state, it is used as a reference state for the excitations to generate the subspace.hermitian_operator (
QubitOperator
) – A Hermitian operator, typically a Hamiltonian, to be expanded in the subspace.expansion_operators (
List
[QubitOperator
]) – A List of excitation operators spanning the subspace.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(*args, **kwargs)¶
Evaluate this object using the provided evaluator function.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class RDM1234RealComputable(space, ansatz, encoding, symmetry_operators, cas_elec, cas_orbs, cu4=True, taperer=None)¶
Bases:
ComputableSingleChild
[List
[ndarray
[Any
,dtype
[_ScalarType_co
]]]]Computable expression for 1,2,3RDMs of a given state, defined by ansatz and parameters.
 Parameters:
space (
FermionSpace
) – Fermion occupation space spanned by this RDM.ansatz (
GeneralAnsatz
) – Ansatz state with respect to which expectation values are computed.encoding (
QubitMapping
) – Fermion to qubit mapping.symmetry_operators (
List
[SymmetryOperatorPauli
]) – Z2 symmetries of the Hamiltonian.cas_elec (
int
) – Number of active electrons.cas_orbs (
int
) – Number of active orbitals.cu4 (
bool
, default:True
) – If True (default), the 4RDM is estimated via the cumulant expansion approximation, otherwise it is measured.taperer (
Optional
[TapererZ2
], default:None
) – TapererZ2 initialized with the Hamiltonian, or None if tapering is not used.
Note
1,2,3,4RDMs are returned as a list of arrays, in PySCFstyle ordering (<p^r^sq>)
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type:
 default_evaluate(parameters, protocol=None)¶
Evaluate the final results immediately for return.
If a protocol is not given it will attempt to use statevector backends from pytketextensions. First, it will try the
AerStateBackend
from pytketqiskit, and then theQulacsBackend
from pytketqulacs. Parameters:
parameters (
SymbolDict
) –SymbolDict
or dict to map symbols to values.protocol (
Optional
[Any
], default:None
) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.
 Returns:
Union
[Evaluatable
,Any
] – Final value of the evaluatable object.
 evaluate(*args, **kwargs)¶
Evaluate this object using the provided evaluator function.
 free_symbols()¶
Returns the union of free symbols from all children.
 Returns:
Set
[Symbol
] – A set containing the free symbols from all children.
 free_symbols_ordered()¶
Returns the free symbols in increasing lexicographic order as
SymbolSet
. Returns:
SymbolSet
– Ordered free symbols in object.
 is_leaf()¶
Check if the current computable node is a leaf (i.e., it has no children).
 Returns:
bool
–True
if the computable node is a leaf,False
otherwise.
 label: str = None¶
 print_tree()¶
Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.
 Return type:
 class RestrictedOneBodyRDMComputable(fermion_space, ansatz, encoding)¶
Bases:
_BaseCollinearOneBodyRDMComputable
Computable expression for a
RestrictedOneBodyRDM
. Parameters:
fermion_space (
FermionSpace
) – Fermion occupation space spanned by this RDM.ansatz (
GeneralAnsatz
) – Ansatz state with respect to which expectation values are computed.encoding (
QubitMapping
) – Fermion to qubit mapping.
 add_label(label, label_children=False)¶
Assign a label to the current computable.
Overwrites any existing label. Access a computable node’s label with
label
. Parameters:
 Returns:
ComputableNode
– Self.
 children()¶
Generator method that yields the child computable nodes of the current computable node.
 Yields:
An iterator over the child computable nodes of the current computable node.
 Return type: