pytket.pauli

This module gives basic Pauli data structures in tket.

enum pytket.pauli.Pauli(value)

Valid values are as follows:

I = Pauli.I

X = Pauli.X

Y = Pauli.Y

Z = Pauli.Z

class pytket.pauli.PauliStabiliser

A string of Pauli letters from the alphabet {I, X, Y, Z} with a +/- 1 coefficient.

__init__(self) → None

__init__(self, string: collections.abc.Sequence[pytket.pauli.Pauli], coeff: int) → None

Overloaded function.

1. __init__(self) -> None

Constructs an empty PauliStabiliser.

2. __init__(self, string: collections.abc.Sequence[pytket.pauli.Pauli], coeff: int) -> None

Constructs a PauliStabiliser with a list of Pauli terms.

property coeff

The coefficient of the stabiliser

property string

The list of Pauli terms

class pytket.pauli.QubitPauliString

A string of Pauli letters from the alphabet {I, X, Y, Z}, implemented as a sparse list, indexed by qubit.

__init__(self) → None

__init__(self, qubit: pytket.unit_id.Qubit, pauli: pytket.pauli.Pauli) → None

__init__(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit], paulis: collections.abc.Sequence[pytket.pauli.Pauli]) → None

__init__(self, map: collections.abc.Mapping[pytket.unit_id.Qubit, pytket.pauli.Pauli]) → None

Overloaded function.

1. __init__(self) -> None

Constructs an empty QubitPauliString.

2. __init__(self, qubit: pytket.unit_id.Qubit, pauli: pytket.pauli.Pauli) -> None

Constructs a QubitPauliString with a single Pauli term.

3. __init__(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit], paulis: collections.abc.Sequence[pytket.pauli.Pauli]) -> None

Constructs a QubitPauliString from two matching lists of Qubits and Paulis.

4. __init__(self, map: collections.abc.Mapping[pytket.unit_id.Qubit, pytket.pauli.Pauli]) -> None

Construct a QubitPauliString from a dictionary mapping Qubit to Pauli.

commutes_with(self, other: pytket.pauli.QubitPauliString) → bool

Returns:

True if the two strings commute, else False

compress(self) → None

Removes I terms to compress the sparse representation.

dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) → numpy.ndarray[dtype=complex128, shape=(*), order='C']

dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → numpy.ndarray[dtype=complex128, shape=(*), order='C']

Overloaded function.

1. dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) -> numpy.ndarray[dtype=complex128, shape=(*), order='C']

Performs the dot product of the state with the pauli string. Maps the qubits of the statevector with sequentially-indexed qubits in the default register, with Qubit(0) being the most significant qubit.

Parameters:

state – statevector for qubits Qubit(0) to Qubit(n-1)

Returns:

dot product of operator with state

2. dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> numpy.ndarray[dtype=complex128, shape=(*), order='C']

Performs the dot product of the state with the pauli string. Maps the qubits of the statevector according to the ordered list qubits, with qubits[0] being the most significant qubit.

Parameters:

• state – statevector

• qubits – order of qubits in state from most to least significant

Returns:

dot product of operator with state

from_list(arg: list, /) → pytket.pauli.QubitPauliString

Construct a new QubitPauliString instance from a JSON serializable list representation.

property map

The QubitPauliString’s underlying dict mapping Qubit to Pauli

state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) → complex

state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → complex

Overloaded function.

1. state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) -> complex

Calculates the expectation value of the state with the pauli string. Maps the qubits of the statevector with sequentially-indexed qubits in the default register, with Qubit(0) being the most significant qubit.

Parameters:

state – statevector for qubits Qubit(0) to Qubit(n-1)

Returns:

expectation value with respect to state

2. state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> complex

Calculates the expectation value of the state with the pauli string. Maps the qubits of the statevector according to the ordered list qubits, with qubits[0] being the most significant qubit.

Parameters:

• state – statevector

• qubits – order of qubits in state from most to least significant

Returns:

expectation value with respect to state

to_list(self) → list

A JSON-serializable representation of the QubitPauliString.

Returns:

a list of Qubit-to-Pauli entries, represented as dicts.

to_sparse_matrix(self) → scipy.sparse.csc_matrix[complex]

to_sparse_matrix(self, n_qubits: int) → scipy.sparse.csc_matrix[complex]

to_sparse_matrix(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → scipy.sparse.csc_matrix[complex]

Overloaded function.

1. to_sparse_matrix(self) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string (without padding for extra qubits) and generates the matrix for the tensor. Uses the ILO-BE convention, so Qubit("a", 0) is more significant that Qubit("a", 1) and Qubit("b") for indexing into the matrix.

Returns:

a sparse matrix corresponding to the operator

2. to_sparse_matrix(self, n_qubits: int) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string over n_qubits qubits (sequentially indexed from 0 in the default register) and generates the matrix for the tensor. Uses the ILO-BE convention, so Qubit(0) is the most significant bit for indexing into the matrix.

Parameters:

n_qubits – the number of qubits in the full operator

Returns:

a sparse matrix corresponding to the operator

3. to_sparse_matrix(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string and generates the matrix for the tensor. Orders qubits according to qubits (padding with identities if they are not in the sparse string), so qubits[0] is the most significant bit for indexing into the matrix.

Parameters:

qubits – the ordered list of qubits in the full operator

Returns:

a sparse matrix corresponding to the operator

class pytket.pauli.QubitPauliTensor

A tensor formed by Pauli terms, consisting of a sparse map from Qubit to Pauli (implemented as a QubitPauliString) and a complex coefficient.

__init__(self, coeff: complex = 1.0) → None

__init__(self, qubit: pytket.unit_id.Qubit, pauli: pytket.pauli.Pauli, coeff: complex = 1.0) → None

__init__(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit], paulis: collections.abc.Sequence[pytket.pauli.Pauli], coeff: complex = 1.0) → None

__init__(self, map: collections.abc.Mapping[pytket.unit_id.Qubit, pytket.pauli.Pauli], coeff: complex = 1.0) → None

__init__(self, string: pytket.pauli.QubitPauliString, coeff: complex = 1.0) → None

Overloaded function.

1. __init__(self, coeff: complex = 1.0) -> None

Constructs an empty QubitPauliTensor, representing the identity.

2. __init__(self, qubit: pytket.unit_id.Qubit, pauli: pytket.pauli.Pauli, coeff: complex = 1.0) -> None

Constructs a QubitPauliTensor with a single Pauli term.

3. __init__(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit], paulis: collections.abc.Sequence[pytket.pauli.Pauli], coeff: complex = 1.0) -> None

Constructs a QubitPauliTensor from two matching lists of Qubits and Paulis.

4. __init__(self, map: collections.abc.Mapping[pytket.unit_id.Qubit, pytket.pauli.Pauli], coeff: complex = 1.0) -> None

Construct a QubitPauliTensor from a dictionary mapping Qubit to Pauli.

5. __init__(self, string: pytket.pauli.QubitPauliString, coeff: complex = 1.0) -> None

Construct a QubitPauliTensor from a QubitPauliString.

property coeff

The global coefficient of the tensor

commutes_with(self, other: pytket.pauli.QubitPauliTensor) → bool

Returns:

True if the two tensors commute, else False

compress(self) → None

Removes I terms to compress the sparse representation.

dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) → numpy.ndarray[dtype=complex128, shape=(*), order='C']

dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → numpy.ndarray[dtype=complex128, shape=(*), order='C']

Overloaded function.

1. dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) -> numpy.ndarray[dtype=complex128, shape=(*), order='C']

Performs the dot product of the state with the pauli tensor. Maps the qubits of the statevector with sequentially-indexed qubits in the default register, with Qubit(0) being the most significant qubit.

Parameters:

state – statevector for qubits Qubit(0) to Qubit(n-1)

Returns:

dot product of operator with state

2. dot_state(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> numpy.ndarray[dtype=complex128, shape=(*), order='C']

Performs the dot product of the state with the pauli tensor. Maps the qubits of the statevector according to the ordered list qubits, with qubits[0] being the most significant qubit.

Parameters:

• state – statevector

• qubits – order of qubits in state from most to least significant

Returns:

dot product of operator with state

state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) → complex

state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → complex

Overloaded function.

1. state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C']) -> complex

Calculates the expectation value of the state with the pauli operator. Maps the qubits of the statevector with sequentially-indexed qubits in the default register, with Qubit(0) being the most significant qubit.

Parameters:

state – statevector for qubits Qubit(0) to Qubit(n-1)

Returns:

expectation value with respect to state

2. state_expectation(self, state: numpy.ndarray[dtype=complex128, shape=(*), order='C'], qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> complex

Calculates the expectation value of the state with the pauli operator. Maps the qubits of the statevector according to the ordered list qubits, with qubits[0] being the most significant qubit.

Parameters:

• state – statevector

• qubits – order of qubits in state from most to least significant

Returns:

expectation value with respect to state

property string

The QubitPauliTensor’s underlying QubitPauliString

to_sparse_matrix(self) → scipy.sparse.csc_matrix[complex]

to_sparse_matrix(self, n_qubits: int) → scipy.sparse.csc_matrix[complex]

to_sparse_matrix(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) → scipy.sparse.csc_matrix[complex]

Overloaded function.

1. to_sparse_matrix(self) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string (without padding for extra qubits) and generates the matrix for the tensor. Uses the ILO-BE convention, so Qubit("a", 0) is more significant that Qubit("a", 1) and Qubit("b") for indexing into the matrix.

Returns:

a sparse matrix corresponding to the tensor

2. to_sparse_matrix(self, n_qubits: int) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string over n_qubits qubits (sequentially indexed from 0 in the default register) and generates the matrix for the tensor. Uses the ILO-BE convention, so Qubit(0) is the most significant bit for indexing into the matrix.

Parameters:

n_qubits – the number of qubits in the full operator

Returns:

a sparse matrix corresponding to the operator

3. to_sparse_matrix(self, qubits: collections.abc.Sequence[pytket.unit_id.Qubit]) -> scipy.sparse.csc_matrix[complex]

Represents the sparse string as a dense string and generates the matrix for the tensor. Orders qubits according to qubits (padding with identities if they are not in the sparse string), so qubits[0] is the most significant bit for indexing into the matrix.

Parameters:

qubits – the ordered list of qubits in the full operator

Returns:

a sparse matrix corresponding to the operator