# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# 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.
"""
Quantum Process Tomography experiment
"""
from typing import Union, Optional, List, Tuple, Sequence
import numpy as np
from qiskit.circuit import QuantumCircuit, Instruction, Clbit
from qiskit.providers.backend import Backend
from qiskit.quantum_info.operators.base_operator import BaseOperator
from qiskit.quantum_info import Choi, Operator, Statevector, DensityMatrix, partial_trace
from qiskit_experiments.exceptions import QiskitError
from .tomography_experiment import TomographyExperiment, TomographyAnalysis, BaseAnalysis
from .qpt_analysis import ProcessTomographyAnalysis
from . import basis
[docs]
class ProcessTomography(TomographyExperiment):
"""An experiment to reconstruct the quantum channel from measurement data.
# section: overview
Quantum process tomography (QPT) is a method for experimentally
reconstructing the quantum channel from measurement data.
A QPT experiment prepares multiple input states, evolves them by the
circuit, then performs multiple measurements in different measurement
bases. The resulting measurement data is then post-processed by a
tomography fitter to reconstruct the quantum channel.
# section: note
Performing full process tomography on an `N`-qubit circuit requires
running :math:`4^N 3^N` measurement circuits when using the default
preparation and measurement bases.
# section: analysis_ref
:class:`ProcessTomographyAnalysis`
# section: example
.. jupyter-execute::
:hide-code:
# backend
from qiskit_aer import AerSimulator
from qiskit_ibm_runtime.fake_provider import FakePerth
backend = AerSimulator.from_backend(FakePerth())
.. jupyter-execute::
import numpy as np
from qiskit import QuantumCircuit
from qiskit_experiments.library import ProcessTomography
num_qubits = 2
qc_ghz = QuantumCircuit(num_qubits)
qc_ghz.h(0)
qc_ghz.s(0)
for i in range(1, num_qubits):
qc_ghz.cx(0, i)
qptexp = ProcessTomography(qc_ghz)
qptdata = qptexp.run(backend=backend,
shots=1000,
seed_simulator=100,).block_for_results()
choi_out = qptdata.analysis_results("state", dataframe=True).iloc[0].value
# extracting a densitymatrix from choi_out
from qiskit.visualization import plot_state_city
import qiskit.quantum_info as qinfo
_rho_exp_00 = np.array([[None, None, None, None],
[None, None, None, None],
[None, None, None, None],
[None, None, None, None]])
for i in range(4):
for j in range(4):
_rho_exp_00[i][j] = choi_out.data[i][j]
rho_exp_00 = qinfo.DensityMatrix(_rho_exp_00)
display(plot_state_city(rho_exp_00, title="Density Matrix"))
"""
def __init__(
self,
circuit: Union[QuantumCircuit, Instruction, BaseOperator],
backend: Optional[Backend] = None,
physical_qubits: Optional[Sequence[int]] = None,
measurement_basis: basis.MeasurementBasis = basis.PauliMeasurementBasis(),
measurement_indices: Optional[Sequence[int]] = None,
preparation_basis: basis.PreparationBasis = basis.PauliPreparationBasis(),
preparation_indices: Optional[Sequence[int]] = None,
basis_indices: Optional[Sequence[Tuple[List[int], List[int]]]] = None,
conditional_circuit_clbits: Union[bool, Sequence[int], Sequence[Clbit]] = False,
analysis: Union[BaseAnalysis, None, str] = "default",
target: Union[Statevector, DensityMatrix, None, str] = "default",
):
"""Initialize a quantum process tomography experiment.
Args:
circuit: the quantum process circuit. If not a quantum circuit
it must be a class that can be appended to a quantum circuit.
backend: The backend to run the experiment on.
physical_qubits: Optional, the physical qubits for the initial state circuit.
If None this will be qubits [0, N) for an N-qubit circuit.
measurement_basis: Tomography basis for measurements. If not specified the
default basis is the :class:`~basis.PauliMeasurementBasis`.
measurement_indices: Optional, the `physical_qubits` indices to be measured.
If None all circuit physical qubits will be measured.
preparation_basis: Tomography basis for measurements. If not specified the
default basis is the :class:`~basis.PauliPreparationBasis`.
preparation_indices: Optional, the `physical_qubits` indices to be prepared.
If None all circuit physical qubits will be prepared.
basis_indices: Optional, a list of basis indices for generating partial
tomography measurement data. Each item should be given as a pair of
lists of preparation and measurement basis configurations
``([p[0], p[1], ...], [m[0], m[1], ...])``, where ``p[i]`` is the
preparation basis index, and ``m[i]`` is the measurement basis index
for qubit-i. If not specified full tomography for all indices of the
preparation and measurement bases will be performed.
conditional_circuit_clbits: Optional, the clbits in the source circuit to
be conditioned on when reconstructing the channel. If True all circuit
clbits will be conditioned on. Enabling this will return a list of
reconstructed channel components conditional on the values of these clbit
values.
analysis: Optional, a custom analysis instance to use. If ``"default"``
:class:`~.ProcessTomographyAnalysis` will be used. If None no analysis
instance will be set.
target: Optional, a custom quantum state target for computing the
state fidelity of the fitted density matrix during analysis.
If "default" the state will be inferred from the input circuit
if it contains no classical instructions.
"""
if analysis == "default":
analysis = ProcessTomographyAnalysis()
super().__init__(
circuit,
backend=backend,
physical_qubits=physical_qubits,
measurement_basis=measurement_basis,
measurement_indices=measurement_indices,
preparation_basis=preparation_basis,
preparation_indices=preparation_indices,
basis_indices=basis_indices,
conditional_circuit_clbits=conditional_circuit_clbits,
analysis=analysis,
)
# Set target quantum channel
if isinstance(self.analysis, TomographyAnalysis):
if target == "default":
target = self._target_quantum_channel()
self.analysis.set_options(target=target)
def _target_quantum_channel(self) -> Union[Choi, Operator]:
"""Return the process tomography target"""
# Check if circuit contains measure instructions
# If so we cannot return target state
circuit_ops = self._circuit.count_ops()
if "measure" in circuit_ops:
return None
try:
circuit = self._permute_circuit()
if "reset" in circuit_ops or "kraus" in circuit_ops or "superop" in circuit_ops:
channel = Choi(circuit)
else:
channel = Operator(circuit)
except QiskitError:
# Circuit couldn't be simulated
return None
total_qubits = self._circuit.num_qubits
num_meas = total_qubits if not self._meas_indices else len(self._meas_indices)
num_prep = total_qubits if not self._prep_indices else len(self._prep_indices)
# If all qubits are prepared or measurement we are done
if num_meas == total_qubits and num_prep == total_qubits:
return channel
# Convert channel to a state to project and trace out non-tomography
# input and output qubits
if isinstance(channel, Operator):
chan_state = Statevector(np.ravel(channel, order="F"))
else:
chan_state = DensityMatrix(channel.data)
# Get qargs for non measured and prepared subsystems
non_meas_qargs = list(range(num_meas, total_qubits))
non_prep_qargs = list(range(total_qubits + num_prep, 2 * total_qubits))
# Project non-prepared subsystems on to the zero state
if non_prep_qargs:
proj0 = Operator([[1, 0], [0, 0]])
for qarg in non_prep_qargs:
chan_state = chan_state.evolve(proj0, [qarg])
# Trace out indices to remove
tr_qargs = non_meas_qargs + non_prep_qargs
chan_state = partial_trace(chan_state, tr_qargs)
channel = Choi(chan_state.data, input_dims=[2] * num_prep, output_dims=[2] * num_meas)
return channel