# 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 State Tomography experiment
"""
from typing import Union, Optional, List, Sequence
from qiskit.providers.backend import Backend
from qiskit.circuit import QuantumCircuit, Instruction, Clbit
from qiskit.quantum_info.operators.base_operator import BaseOperator
from qiskit.quantum_info import Statevector, DensityMatrix, partial_trace
from qiskit_experiments.exceptions import QiskitError
from .tomography_experiment import TomographyExperiment, TomographyAnalysis, BaseAnalysis
from .qst_analysis import StateTomographyAnalysis
from . import basis
[docs]
class StateTomography(TomographyExperiment):
"""An experiment to reconstruct the quantum state from measurement data.
# section: overview
Quantum state tomography (QST) is a method for experimentally
reconstructing the quantum state from measurement data.
A QST experiment measures the state prepared by quantum
circuit in different measurement bases and post-processes the
measurement data to reconstruct the state.
# section: note
Performing full state tomography on an `N`-qubit state requires
running :math:`3^N` measurement circuits when using the default
measurement basis.
# section: analysis_ref
:class:`StateTomographyAnalysis`
# section: manual
:doc:`/manuals/verification/state_tomography`
# 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::
from qiskit import QuantumCircuit
from qiskit_experiments.library import StateTomography
from qiskit.visualization import plot_state_city
nq = 2
qc_ghz = QuantumCircuit(nq)
qc_ghz.h(0)
qc_ghz.s(0)
for i in range(1, nq):
qc_ghz.cx(0, i)
qstexp = StateTomography(qc_ghz)
qstdata = qstexp.run(backend=backend,
shots=1000,
seed_simulator=100,).block_for_results()
state_result = qstdata.analysis_results("state", dataframe=True).iloc[0]
plot_state_city(state_result.value, title="Density Matrix")
"""
def __init__(
self,
circuit: Union[QuantumCircuit, Instruction, BaseOperator, Statevector],
backend: Optional[Backend] = None,
physical_qubits: Optional[Sequence[int]] = None,
measurement_basis: basis.MeasurementBasis = basis.PauliMeasurementBasis(),
measurement_indices: Optional[Sequence[int]] = None,
basis_indices: Optional[Sequence[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.
basis_indices: Optional, a list of basis indices for generating partial
tomography measurement data. Each item should be given as a list of
measurement basis configurations ``[m[0], m[1], ...]`` where ``m[i]``
is the measurement basis index for qubit-i. If not specified full
tomography for all indices of the measurement basis will be performed.
conditional_circuit_clbits: Optional, the clbits in the source circuit to
be conditioned on when reconstructing the state. If True all circuit
clbits will be conditioned on. Enabling this will return a list of
reconstructed state components conditional on the values of these clbit
values.
analysis: Optional, a custom analysis instance to use. If ``"default"``
:class:`~.StateTomographyAnalysis` 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 isinstance(circuit, Statevector):
# Convert to circuit using initialize instruction
circ = QuantumCircuit(circuit.num_qubits)
circ.initialize(circuit)
circuit = circ
if basis_indices is not None:
# Add trivial preparation indices for base class
basis_indices = [([], i) for i in basis_indices]
if analysis == "default":
analysis = StateTomographyAnalysis()
super().__init__(
circuit,
backend=backend,
physical_qubits=physical_qubits,
measurement_basis=measurement_basis,
measurement_indices=measurement_indices,
basis_indices=basis_indices,
conditional_circuit_clbits=conditional_circuit_clbits,
analysis=analysis,
)
# Set target quantum state
if isinstance(self.analysis, TomographyAnalysis):
if target == "default":
target = self._target_quantum_state()
self.analysis.set_options(target=target)
def _target_quantum_state(self) -> Union[Statevector, DensityMatrix]:
"""Return the state 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:
state = DensityMatrix(circuit)
else:
state = Statevector(circuit)
except QiskitError:
# Circuit couldn't be simulated
return None
if not self._meas_indices:
return state
non_meas_qargs = list(range(len(self._meas_indices), self._circuit.num_qubits))
if non_meas_qargs:
# Trace over non-measured qubits
state = partial_trace(state, non_meas_qargs)
return state