# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2021, 2023.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""The Bravyi-Kitaev Mapper."""
from __future__ import annotations
from functools import lru_cache
import numpy as np
from qiskit.quantum_info.operators import Pauli
from .fermionic_mapper import FermionicMapper
[docs]class BravyiKitaevMapper(FermionicMapper):
"""The Bravyi-Kitaev fermion-to-qubit mapping."""
[docs] @classmethod
@lru_cache(maxsize=32)
def pauli_table(cls, register_length: int) -> list[tuple[Pauli, Pauli]]:
# pylint: disable=unused-argument
def parity_set(j, n):
"""
Computes the parity set of the j-th orbital in n modes.
Args:
j (int) : the orbital index
n (int) : the total number of modes
Returns:
numpy.ndarray: Array of mode indices
"""
indices = np.array([])
if n % 2 != 0:
return indices
if j < n / 2:
indices = np.append(indices, parity_set(j, n / 2))
else:
indices = np.append(
indices, np.append(parity_set(j - n / 2, n / 2) + n / 2, n / 2 - 1)
)
return indices
def update_set(j, n):
"""
Computes the update set of the j-th orbital in n modes.
Args:
j (int) : the orbital index
n (int) : the total number of modes
Returns:
numpy.ndarray: Array of mode indices
"""
indices = np.array([])
if n % 2 != 0:
return indices
if j < n / 2:
indices = np.append(indices, np.append(n - 1, update_set(j, n / 2)))
else:
indices = np.append(indices, update_set(j - n / 2, n / 2) + n / 2)
return indices
def flip_set(j, n):
"""
Computes the flip set of the j-th orbital in n modes.
Args:
j (int) : the orbital index
n (int) : the total number of modes
Returns:
numpy.ndarray: Array of mode indices
"""
indices = np.array([])
if n % 2 != 0:
return indices
if j < n / 2:
indices = np.append(indices, flip_set(j, n / 2))
elif n / 2 <= j < n - 1:
indices = np.append(indices, flip_set(j - n / 2, n / 2) + n / 2)
else:
indices = np.append(
np.append(indices, flip_set(j - n / 2, n / 2) + n / 2), n / 2 - 1
)
return indices
pauli_table = []
# FIND BINARY SUPERSET SIZE
bin_sup = 1
while register_length > np.power(2, bin_sup):
bin_sup += 1
# DEFINE INDEX SETS FOR EVERY FERMIONIC MODE
update_sets = []
update_pauli = []
parity_sets = []
parity_pauli = []
flip_sets = []
remainder_sets = []
remainder_pauli = []
for j in range(register_length):
update_sets.append(update_set(j, np.power(2, bin_sup)))
update_sets[j] = update_sets[j][update_sets[j] < register_length]
parity_sets.append(parity_set(j, np.power(2, bin_sup)))
parity_sets[j] = parity_sets[j][parity_sets[j] < register_length]
flip_sets.append(flip_set(j, np.power(2, bin_sup)))
flip_sets[j] = flip_sets[j][flip_sets[j] < register_length]
remainder_sets.append(np.setdiff1d(parity_sets[j], flip_sets[j]))
update_pauli.append(
Pauli(
(np.zeros(register_length, dtype=bool), np.zeros(register_length, dtype=bool))
)
)
parity_pauli.append(
Pauli(
(np.zeros(register_length, dtype=bool), np.zeros(register_length, dtype=bool))
)
)
remainder_pauli.append(
Pauli(
(np.zeros(register_length, dtype=bool), np.zeros(register_length, dtype=bool))
)
)
for k in range(register_length):
if np.in1d(k, update_sets[j]):
update_pauli[j].x[k] = True
if np.in1d(k, parity_sets[j]):
parity_pauli[j].z[k] = True
if np.in1d(k, remainder_sets[j]):
remainder_pauli[j].z[k] = True
x_j = Pauli(
(np.zeros(register_length, dtype=bool), np.zeros(register_length, dtype=bool))
)
x_j.x[j] = True
y_j = Pauli(
(np.zeros(register_length, dtype=bool), np.zeros(register_length, dtype=bool))
)
y_j.z[j] = True
y_j.x[j] = True
pauli_table.append(
(
parity_pauli[j] & x_j & update_pauli[j],
remainder_pauli[j] & y_j & update_pauli[j],
)
)
# PauliList has the phase information.
# Here, phase is unnecessary, so the following removes phase.
for pauli1, pauli2 in pauli_table:
pauli1.phase = 0
pauli2.phase = 0
return pauli_table