# Copyright (C) 2021 Unitary Fund
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
"""Qiskit utility functions."""
import numpy as np
import qiskit
from qiskit import QuantumCircuit
from typing import Optional
# Noise simulation packages
from qiskit.providers.aer.noise import NoiseModel
from qiskit.providers.aer.noise.errors.standard_errors import (
depolarizing_error,
)
[docs]def initialized_depolarizing_noise(noise_level: float) -> NoiseModel:
"""Initializes a depolarizing noise Qiskit NoiseModel.
Args:
noise_level: The noise strength as a float, e.g., 0.01 is 0.1%.
Returns:
A Qiskit depolarizing NoiseModel.
"""
# initialize a qiskit noise model
noise_model = NoiseModel()
# we assume the same depolarizing error for each
# gate of the standard IBM basis
noise_model.add_all_qubit_quantum_error(
depolarizing_error(noise_level, 1), ["u1", "u2", "u3"]
)
noise_model.add_all_qubit_quantum_error(
depolarizing_error(noise_level, 2), ["cx"]
)
return noise_model
[docs]def execute(circuit: QuantumCircuit, obs: np.ndarray) -> float:
"""Simulates a noiseless evolution and returns the
expectation value of some observable.
Args:
circuit: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.
Returns:
The expectation value of obs as a float.
"""
return execute_with_noise(circuit, obs, noise_model=None)
[docs]def execute_with_shots(
circuit: QuantumCircuit, obs: np.ndarray, shots: int
) -> float:
"""Simulates the evolution of the circuit and returns
the expectation value of the observable.
Args:
circuit: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.
shots: The number of measurements.
Returns:
The expectation value of obs as a float.
"""
return execute_with_shots_and_noise(
circuit, obs, noise_model=None, shots=shots,
)
[docs]def execute_with_noise(
circuit: QuantumCircuit, obs: np.ndarray, noise_model: NoiseModel
) -> float:
"""Simulates the evolution of the noisy circuit and returns
the exact expectation value of the observable.
Args:
circuit: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.
noise_model: The input Qiskit noise model.
Returns:
The expectation value of obs as a float.
"""
# Avoid mutating circuit
circ = circuit.copy()
circ.save_density_matrix()
if noise_model is None:
basis_gates = None
else:
basis_gates = noise_model.basis_gates + ["save_density_matrix"]
# execution of the experiment
job = qiskit.execute(
circ,
backend=qiskit.Aer.get_backend("aer_simulator_density_matrix"),
noise_model=noise_model,
basis_gates=basis_gates,
# we want all gates to be actually applied,
# so we skip any circuit optimization
optimization_level=0,
shots=1,
)
rho = job.result().data()["density_matrix"]
expectation = np.real(np.trace(rho @ obs))
return expectation
[docs]def execute_with_shots_and_noise(
circuit: QuantumCircuit,
obs: np.ndarray,
noise_model: NoiseModel,
shots: int,
seed: Optional[int] = None,
) -> float:
"""Simulates the evolution of the noisy circuit and returns
the statistical estimate of the expectation value of the observable.
Args:
circuit: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.
noise: The input Qiskit noise model.
shots: The number of measurements.
seed: Optional seed for qiskit simulator.
Returns:
The expectation value of obs as a float.
"""
# Avoid mutating circuit
circ = circuit.copy()
# we need to modify the circuit to measure obs in its eigenbasis
# we do this by appending a unitary operation
# obtains a U s.t. obs = U diag(eigvals) U^dag
eigvals, U = np.linalg.eigh(obs)
circ.unitary(np.linalg.inv(U), qubits=range(circ.num_qubits))
circ.measure_all()
if noise_model is None:
basis_gates = None
else:
basis_gates = noise_model.basis_gates
# execution of the experiment
job = qiskit.execute(
circ,
backend=qiskit.Aer.get_backend("aer_simulator"),
backend_options={"method": "density_matrix"},
noise_model=noise_model,
# we want all gates to be actually applied,
# so we skip any circuit optimization
basis_gates=basis_gates,
optimization_level=0,
shots=shots,
seed_simulator=seed,
)
counts = job.result().get_counts()
expectation = 0
for bitstring, count in counts.items():
expectation += (
eigvals[int(bitstring[0 : circ.num_qubits], 2)] * count / shots
)
return expectation