r"""Computation (noiseless statevector) the full GF matrix of the Hubbard dimer at a single frequency."""

# imports
import numpy as np

from pytket.extensions.qiskit import AerStateBackend

from inquanto.computables.composite import ManyBodyGFComputable
from inquanto.express import DriverHubbardDimer
from inquanto.operators import FermionOperator
from inquanto.ansatzes import FermionSpaceAnsatzChemicallyAwareUCCSD
from inquanto.express import run_vqe


# define Hamiltonian H (here we use Hubbard dimer at half filling). Note t is negated in DriverHubbardDimer
u_hub = 2.15
t_hub = 0.3
n_sites = 2
driver = DriverHubbardDimer(t=t_hub, u=u_hub)

# get fermionic ham, space, and state from driver
h, space, state = driver.get_system()
# we can print the hamiltonian for inspection
# print(h.df())

# create set of one-body excitation operators
n1u = FermionOperator(((space.index(0, 0), 1), (space.index(0, 0), 0)))
n1d = FermionOperator(((space.index(0, 1), 1), (space.index(0, 1), 0)))
n2u = FermionOperator(((space.index(1, 0), 1), (space.index(1, 0), 0)))
n2d = FermionOperator(((space.index(1, 1), 1), (space.index(1, 1), 0)))

# this sets the chemical potential to -U/2 in the Hamiltonian
# and adds the set of created operators
h -= 0.5 * u_hub * (n1u + n1d + n2u + n2d)

# add a constant term
h += 0.5 * FermionOperator.identity() * u_hub
# print(h.df())

# Jordan-Wigner encode the extended dimer hamiltonian
qubit_hamiltonian = h.qubit_encode()

# get the exact ground state energy, to be compared with VQE energy
print(
    "Exact gs energy:",
    qubit_hamiltonian.eigenspectrum(state.single_term.hamming_weight)[0],
)

# instantiate the ansatz using the fermion space and state
ansatz = FermionSpaceAnsatzChemicallyAwareUCCSD(space, state)

# prepare a dictionary to parameterize the ansatz
parameters = ansatz.state_symbols.construct_random(2, 0.01, 0.1)

# backend for ideal noiseless statevector calculations
backend = AerStateBackend()

# run VQE, compare energy to exact value (get good approximation to ground state here), and store final parameters
vqe = run_vqe(
    ansatz,
    qubit_hamiltonian,
    backend,
    with_gradient=False,
    initial_parameters=parameters,
)
energy = vqe.generate_report()["final_value"]
print("Minimum Energy: {}".format(energy))
final_parameters = vqe.final_parameters

# MBGF computable
# select dimension of Krylov space (2 sufficient for symmetric Hubbard dimer)
n_lanczos_roots = 2

# instantiate the GF Computable, and evaluate matrix (its size is determined by space), omega symbolic
gf_class = ManyBodyGFComputable(
    space,
    ansatz,
    qubit_hamiltonian,
    n_lanczos_roots,
    ground_state_energy=energy,
    eta=0.00,
)

# default evaluate uses protocol for noiseless statevector calculations
gf_object_matrix_func = gf_class.default_evaluate_as_function(final_parameters)

# plug in a value (possibly imaginary) for omega (frequency), to numerically evaluate the matrix
gf_matrix = gf_object_matrix_func(0.3j)
np.set_printoptions(linewidth=1000)
print("\nquantum GF matrix\n", gf_matrix)