Source code for qiskit_algorithms.phase_estimators.phase_estimation

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"""The Quantum Phase Estimation Algorithm."""

from __future__ import annotations

import numpy
import qiskit
from qiskit import circuit
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.classicalregister import ClassicalRegister
from qiskit.primitives import BaseSampler
from qiskit.result import Result

from qiskit_algorithms.exceptions import AlgorithmError

from .phase_estimation_result import PhaseEstimationResult, _sort_phases
from .phase_estimator import PhaseEstimator

[docs]class PhaseEstimation(PhaseEstimator): r"""Run the Quantum Phase Estimation (QPE) algorithm. This runs QPE with a multi-qubit register for reading the phases [1] of input states. The algorithm takes as input a unitary :math:`U` and a state :math:`|\psi\rangle`, which may be written .. math:: |\psi\rangle = \sum_j c_j |\phi_j\rangle, where :math:`|\phi_j\rangle` are eigenstates of :math:`U`. We prepare the quantum register in the state :math:`|\psi\rangle` then apply :math:`U` leaving the register in the state .. math:: U|\psi\rangle = \sum_j \exp(i \phi_j) c_j |\phi_j\rangle. In the ideal case, one then measures the phase :math:`\phi_j` with probability :math:`|c_j|^2`. In practice, many (or all) of the bit strings may be measured due to noise and the possibility that :math:`\phi_j` may not be representable exactly by the output register. In the latter case the probability for each eigenphase will be spread across bitstrings, with amplitudes that decrease with distance from the bitstring most closely approximating the eigenphase. The main input to the constructor is the number of qubits in the phase-reading register. For phase estimation, there are two methods: first. `estimate`, which takes a state preparation circuit to prepare an input state, and a unitary that will act on the input state. In this case, an instance of :class:`qiskit.circuit.PhaseEstimation`, a QPE circuit, containing the state preparation and input unitary will be constructed. second. `estimate_from_pe_circuit`, which takes a quantum-phase-estimation circuit in which the unitary and state preparation are already embedded. In both estimation methods, the QPE circuit is run on a backend and the frequencies or counts of the phases represented by bitstrings are recorded. The results are returned as an instance of :class:`~qiskit_algorithms.phase_estimator_result.PhaseEstimationResult`. **Reference:** [1]: Michael A. Nielsen and Isaac L. Chuang. 2011. Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.). Cambridge University Press, New York, NY, USA. """ def __init__( self, num_evaluation_qubits: int, sampler: BaseSampler | None = None, ) -> None: r""" Args: num_evaluation_qubits: The number of qubits used in estimating the phase. The phase will be estimated as a binary string with this many bits. sampler: The sampler primitive on which the circuit will be sampled. Raises: AlgorithmError: If a sampler is not provided """ if sampler is None: raise AlgorithmError("A sampler must be provided.") self._measurements_added = False if num_evaluation_qubits is not None: self._num_evaluation_qubits = num_evaluation_qubits self._sampler = sampler
[docs] def construct_circuit( self, unitary: QuantumCircuit, state_preparation: QuantumCircuit | None = None ) -> QuantumCircuit: """Return the circuit to be executed to estimate phases. This circuit includes as sub-circuits the core phase estimation circuit, with the addition of the state-preparation circuit and possibly measurement instructions. """ num_evaluation_qubits = self._num_evaluation_qubits num_unitary_qubits = unitary.num_qubits pe_circuit = circuit.library.PhaseEstimation(num_evaluation_qubits, unitary) if state_preparation is not None: pe_circuit.compose( state_preparation, qubits=range(num_evaluation_qubits, num_evaluation_qubits + num_unitary_qubits), inplace=True, front=True, ) return pe_circuit
def _add_measurement_if_required(self, pe_circuit): # Measure only the evaluation qubits. regname = "meas" creg = ClassicalRegister(self._num_evaluation_qubits, regname) pe_circuit.add_register(creg) pe_circuit.barrier() pe_circuit.measure(range(self._num_evaluation_qubits), range(self._num_evaluation_qubits)) return circuit def _compute_phases(self, circuit_result: Result) -> numpy.ndarray | qiskit.result.Counts: """Compute frequencies/counts of phases from the result of running the QPE circuit. How the frequencies are computed depends on whether the backend computes amplitude or samples outcomes. 1) If the backend is a statevector simulator, then the reduced density matrix of the phase-reading register is computed from the combined phase-reading- and input-state registers. The elements of the diagonal :math:`(i, i)` give the probability to measure the each of the states `i`. The index `i` expressed as a binary integer with the LSB rightmost gives the state of the phase-reading register with the LSB leftmost when interpreted as a phase. In order to maintain the compact representation, the phases are maintained as decimal integers. They may be converted to other forms via the results object, `PhaseEstimationResult` or `HamiltonianPhaseEstimationResult`. 2) If the backend samples bitstrings, then the counts are first retrieved as a dict. The binary strings (the keys) are then reversed so that the LSB is rightmost and the counts are converted to frequencies. Then the keys are sorted according to increasing phase, so that they can be easily understood when displaying or plotting a histogram. Args: num_unitary_qubits: The number of qubits in the unitary. circuit_result: the result object returned by the backend that ran the QPE circuit. Returns: Either a dict or numpy.ndarray representing the frequencies of the phases. """ # return counts with keys sorted numerically num_shots = circuit_result.results[0].shots counts = circuit_result.get_counts() phases = {k[::-1]: counts[k] / num_shots for k in counts.keys()} phases = _sort_phases(phases) phases = qiskit.result.Counts( phases, memory_slots=counts.memory_slots, creg_sizes=counts.creg_sizes ) return phases
[docs] def estimate_from_pe_circuit(self, pe_circuit: QuantumCircuit) -> PhaseEstimationResult: """Run the phase estimation algorithm on a phase estimation circuit Args: pe_circuit: The phase estimation circuit. Returns: A phase estimation result. Raises: AlgorithmError: Primitive job failed. """ self._add_measurement_if_required(pe_circuit) try: circuit_job =[pe_circuit]) circuit_result = circuit_job.result() except Exception as exc: raise AlgorithmError("The primitive job failed!") from exc phases = circuit_result.quasi_dists[0] phases_bitstrings = {} for key, phase in phases.items(): bitstring_key = self._get_reversed_bitstring(self._num_evaluation_qubits, key) phases_bitstrings[bitstring_key] = phase phases = phases_bitstrings return PhaseEstimationResult( self._num_evaluation_qubits, circuit_result=circuit_result, phases=phases )
[docs] def estimate( self, unitary: QuantumCircuit, state_preparation: QuantumCircuit | None = None, ) -> PhaseEstimationResult: """Build a phase estimation circuit and run the corresponding algorithm. Args: unitary: The circuit representing the unitary operator whose eigenvalues (via phase) will be measured. state_preparation: The circuit that prepares the state whose eigenphase will be measured. If this parameter is omitted, no preparation circuit will be run and input state will be the all-zero state in the computational basis. Returns: A phase estimation result. """ pe_circuit = self.construct_circuit(unitary, state_preparation) return self.estimate_from_pe_circuit(pe_circuit)