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Source code for qiskit_optimization.algorithms.grover_optimizer

# This code is part of Qiskit.
#
# (C) Copyright IBM 2020, 2022.
#
# 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.

"""GroverOptimizer module"""

import logging
import math
import warnings
from copy import deepcopy
from typing import Dict, List, Optional, Union, cast

import numpy as np
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.algorithms import AmplificationProblem
from qiskit.algorithms.amplitude_amplifiers.grover import Grover
from qiskit.circuit.library import QuadraticForm
from qiskit.primitives import BaseSampler
from qiskit.providers import Backend
from qiskit.quantum_info import partial_trace
from qiskit.utils import QuantumInstance, algorithm_globals

from ..converters.quadratic_program_to_qubo import QuadraticProgramConverter, QuadraticProgramToQubo
from ..exceptions import QiskitOptimizationError
from ..problems import Variable
from ..problems.quadratic_program import QuadraticProgram
from .optimization_algorithm import (
    OptimizationAlgorithm,
    OptimizationResult,
    OptimizationResultStatus,
    SolutionSample,
)

logger = logging.getLogger(__name__)


[docs]class GroverOptimizer(OptimizationAlgorithm): """Uses Grover Adaptive Search (GAS) to find the minimum of a QUBO function.""" def __init__( self, num_value_qubits: int, num_iterations: int = 3, quantum_instance: Optional[Union[Backend, QuantumInstance]] = None, converters: Optional[ Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] ] = None, penalty: Optional[float] = None, sampler: Optional[BaseSampler] = None, ) -> None: """ Args: num_value_qubits: The number of value qubits. num_iterations: The number of iterations the algorithm will search with no improvement. quantum_instance: Instance of selected backend, defaults to Aer's statevector simulator. converters: The converters to use for converting a problem into a different form. By default, when None is specified, an internally created instance of :class:`~qiskit_optimization.converters.QuadraticProgramToQubo` will be used. penalty: The penalty factor used in the default :class:`~qiskit_optimization.converters.QuadraticProgramToQubo` converter sampler: A Sampler to use for sampling the results of the circuits. Raises: ValueError: If both a quantum instance and sampler are set. TypeError: When there one of converters is an invalid type. """ self._num_value_qubits = num_value_qubits self._num_key_qubits = 0 self._n_iterations = num_iterations self._circuit_results = {} # type: dict self._converters = self._prepare_converters(converters, penalty) if quantum_instance is not None and sampler is not None: raise ValueError("Only one of quantum_instance or sampler can be passed, not both!") self._quantum_instance = None # type: Optional[QuantumInstance] if quantum_instance is not None: warnings.warn( "The quantum_instance argument has been superseded by the sampler argument. " "This argument will be deprecated in a future release and subsequently " "removed after that.", category=PendingDeprecationWarning, stacklevel=2, ) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=PendingDeprecationWarning) self.quantum_instance = quantum_instance self._sampler = sampler @property def quantum_instance(self) -> QuantumInstance: """The quantum instance to run the circuits. Returns: The quantum instance used in the algorithm. """ warnings.warn( "The quantum_instance argument has been superseded by the sampler argument. " "This argument will be deprecated in a future release and subsequently " "removed after that.", category=PendingDeprecationWarning, stacklevel=2, ) return self._quantum_instance @quantum_instance.setter def quantum_instance(self, quantum_instance: Union[Backend, QuantumInstance]) -> None: """Set the quantum instance used to run the circuits. Args: quantum_instance: The quantum instance to be used in the algorithm. """ warnings.warn( "The GroverOptimizer.quantum_instance setter is pending deprecation. " "This property will be deprecated in a future release and subsequently " "removed after that.", category=PendingDeprecationWarning, stacklevel=2, ) if isinstance(quantum_instance, Backend): self._quantum_instance = QuantumInstance(quantum_instance) else: self._quantum_instance = quantum_instance
[docs] def get_compatibility_msg(self, problem: QuadraticProgram) -> str: """Checks whether a given problem can be solved with this optimizer. Checks whether the given problem is compatible, i.e., whether the problem can be converted to a QUBO, and otherwise, returns a message explaining the incompatibility. Args: problem: The optimization problem to check compatibility. Returns: A message describing the incompatibility. """ return QuadraticProgramToQubo.get_compatibility_msg(problem)
def _get_a_operator(self, qr_key_value, problem): quadratic = problem.objective.quadratic.to_array() linear = problem.objective.linear.to_array() offset = problem.objective.constant # Get circuit requirements from input. quadratic_form = QuadraticForm( self._num_value_qubits, quadratic, linear, offset, little_endian=False ) a_operator = QuantumCircuit(qr_key_value) a_operator.h(list(range(self._num_key_qubits))) a_operator.compose(quadratic_form, inplace=True) return a_operator def _get_oracle(self, qr_key_value): # Build negative value oracle O. if qr_key_value is None: qr_key_value = QuantumRegister(self._num_key_qubits + self._num_value_qubits) oracle_bit = QuantumRegister(1, "oracle") oracle = QuantumCircuit(qr_key_value, oracle_bit) oracle.z(self._num_key_qubits) # recognize negative values. def is_good_state(measurement): """Check whether ``measurement`` is a good state or not.""" value = measurement[ self._num_key_qubits : self._num_key_qubits + self._num_value_qubits ] return value[0] == "1" return oracle, is_good_state
[docs] def solve(self, problem: QuadraticProgram) -> OptimizationResult: """Tries to solves the given problem using the grover optimizer. Runs the optimizer to try to solve the optimization problem. If the problem cannot be, converted to a QUBO, this optimizer raises an exception due to incompatibility. Args: problem: The problem to be solved. Returns: The result of the optimizer applied to the problem. Raises: ValueError: If a quantum instance or a sampler has not been provided. ValueError: If both a quantum instance and sampler are set. AttributeError: If the quantum instance has not been set. QiskitOptimizationError: If the problem is incompatible with the optimizer. """ if self._sampler is None and self._quantum_instance is None: raise ValueError("A quantum instance or sampler must be provided.") if self._quantum_instance is not None and self._sampler is not None: raise ValueError("Only one of quantum_instance or sampler can be passed, not both!") self._verify_compatibility(problem) # convert problem to minimization QUBO problem problem_ = self._convert(problem, self._converters) problem_init = deepcopy(problem_) self._num_key_qubits = len(problem_.objective.linear.to_array()) # Variables for tracking the optimum. optimum_found = False optimum_key = math.inf optimum_value = math.inf threshold = 0 n_key = self._num_key_qubits n_value = self._num_value_qubits # Variables for tracking the solutions encountered. num_solutions = 2**n_key keys_measured = [] # Variables for result object. operation_count = {} iteration = 0 # Variables for stopping if we've hit the rotation max. rotations = 0 max_rotations = int(np.ceil(100 * np.pi / 4)) # Initialize oracle helper object. qr_key_value = QuantumRegister(self._num_key_qubits + self._num_value_qubits) orig_constant = problem_.objective.constant measurement = self._quantum_instance is None or not self._quantum_instance.is_statevector oracle, is_good_state = self._get_oracle(qr_key_value) while not optimum_found: m = 1 improvement_found = False # Get oracle O and the state preparation operator A for the current threshold. problem_.objective.constant = orig_constant - threshold a_operator = self._get_a_operator(qr_key_value, problem_) # Iterate until we measure a negative. loops_with_no_improvement = 0 while not improvement_found: # Determine the number of rotations. loops_with_no_improvement += 1 rotation_count = algorithm_globals.random.integers(0, m) rotations += rotation_count # Apply Grover's Algorithm to find values below the threshold. # TODO: Utilize Grover's incremental feature - requires changes to Grover. amp_problem = AmplificationProblem( oracle=oracle, state_preparation=a_operator, is_good_state=is_good_state, ) grover = Grover() circuit = grover.construct_circuit( problem=amp_problem, power=rotation_count, measurement=measurement ) # Get the next outcome. outcome = self._measure(circuit) k = int(outcome[0:n_key], 2) v = outcome[n_key : n_key + n_value] int_v = self._bin_to_int(v, n_value) + threshold logger.info("Outcome: %s", outcome) logger.info("Value Q(x): %s", int_v) # If the value is an improvement, we update the iteration parameters (e.g. oracle). if int_v < optimum_value: optimum_key = k optimum_value = int_v logger.info("Current Optimum Key: %s", optimum_key) logger.info("Current Optimum Value: %s", optimum_value) improvement_found = True threshold = optimum_value # trace out work qubits and store samples if self._sampler is not None: self._circuit_results = { i[-1 * n_key :]: v for i, v in self._circuit_results.items() } else: if self._quantum_instance.is_statevector: indices = list(range(n_key, len(outcome))) rho = partial_trace(self._circuit_results, indices) self._circuit_results = cast(Dict, np.diag(rho.data) ** 0.5) else: self._circuit_results = { i[-1 * n_key :]: v for i, v in self._circuit_results.items() } raw_samples = self._eigenvector_to_solutions( self._circuit_results, problem_init ) raw_samples.sort(key=lambda x: x.fval) samples, _ = self._interpret_samples(problem, raw_samples, self._converters) else: # Using Durr and Hoyer method, increase m. m = int(np.ceil(min(m * 8 / 7, 2 ** (n_key / 2)))) logger.info("No Improvement. M: %s", m) # Check if we've already seen this value. if k not in keys_measured: keys_measured.append(k) # Assume the optimal if any of the stop parameters are true. if ( loops_with_no_improvement >= self._n_iterations or len(keys_measured) == num_solutions or rotations >= max_rotations ): improvement_found = True optimum_found = True # Track the operation count. operations = circuit.count_ops() operation_count[iteration] = operations iteration += 1 logger.info("Operation Count: %s\n", operations) # If the constant is 0 and we didn't find a negative, the answer is likely 0. if optimum_value >= 0 and orig_constant == 0: optimum_key = 0 opt_x = np.array([1 if s == "1" else 0 for s in f"{optimum_key:{n_key}b}"]) # Compute function value of minimization QUBO fval = problem_init.objective.evaluate(opt_x) # cast binaries back to integers and eventually minimization to maximization return cast( GroverOptimizationResult, self._interpret( x=opt_x, converters=self._converters, problem=problem, result_class=GroverOptimizationResult, samples=samples, raw_samples=raw_samples, operation_counts=operation_count, n_input_qubits=n_key, n_output_qubits=n_value, intermediate_fval=fval, threshold=threshold, ), )
def _measure(self, circuit: QuantumCircuit) -> str: """Get probabilities from the given backend, and picks a random outcome.""" probs = self._get_prob_dist(circuit) logger.info("Frequencies: %s", probs) # Pick a random outcome. return algorithm_globals.random.choice(list(probs.keys()), 1, p=list(probs.values()))[0] def _get_prob_dist(self, qc: QuantumCircuit) -> Dict[str, float]: """Gets probabilities from a given backend.""" # Execute job and filter results. if self._sampler is not None: job = self._sampler.run([qc]) try: result = job.result() except Exception as exc: raise QiskitOptimizationError("Sampler job failed.") from exc quasi_dist = result.quasi_dists[0] raw_prob_dist = { k: v for k, v in quasi_dist.binary_probabilities(qc.num_qubits).items() if v >= self._MIN_PROBABILITY } prob_dist = {k[::-1]: v for k, v in raw_prob_dist.items()} self._circuit_results = {i: v**0.5 for i, v in raw_prob_dist.items()} else: result = self._quantum_instance.execute(qc) if self._quantum_instance.is_statevector: state = result.get_statevector(qc) if not isinstance(state, np.ndarray): state = state.data keys = [ bin(i)[2::].rjust(int(np.log2(len(state))), "0")[::-1] for i in range(0, len(state)) ] probs = [abs(a) ** 2 for a in state] total = math.fsum(probs) probs = [p / total for p in probs] prob_dist = {key: prob for key, prob in zip(keys, probs) if prob > 0} self._circuit_results = state else: state = result.get_counts(qc) shots = self._quantum_instance.run_config.shots prob_dist = { key[::-1]: val / shots for key, val in sorted(state.items()) if val > 0 } self._circuit_results = {b: (v / shots) ** 0.5 for (b, v) in state.items()} return prob_dist @staticmethod def _bin_to_int(v: str, num_value_bits: int) -> int: """Converts a binary string of n bits using two's complement to an integer.""" if v.startswith("1"): int_v = int(v, 2) - 2**num_value_bits else: int_v = int(v, 2) return int_v
[docs]class GroverOptimizationResult(OptimizationResult): """A result object for Grover Optimization methods.""" def __init__( self, x: Union[List[float], np.ndarray], fval: float, variables: List[Variable], operation_counts: Dict[int, Dict[str, int]], n_input_qubits: int, n_output_qubits: int, intermediate_fval: float, threshold: float, status: OptimizationResultStatus, samples: Optional[List[SolutionSample]] = None, raw_samples: Optional[List[SolutionSample]] = None, ) -> None: """ Constructs a result object with the specific Grover properties. Args: x: The solution of the problem fval: The value of the objective function of the solution variables: A list of variables defined in the problem operation_counts: The counts of each operation performed per iteration. n_input_qubits: The number of qubits used to represent the input. n_output_qubits: The number of qubits used to represent the output. intermediate_fval: The intermediate value of the objective function of the minimization qubo solution, that is expected to be consistent to ``fval``. threshold: The threshold of Grover algorithm. status: the termination status of the optimization algorithm. samples: the x values, the objective function value of the original problem, the probability, and the status of sampling. raw_samples: the x values of the QUBO, the objective function value of the minimization QUBO, and the probability of sampling. """ super().__init__( x=x, fval=fval, variables=variables, status=status, raw_results=None, samples=samples, ) self._raw_samples = raw_samples self._operation_counts = operation_counts self._n_input_qubits = n_input_qubits self._n_output_qubits = n_output_qubits self._intermediate_fval = intermediate_fval self._threshold = threshold @property def operation_counts(self) -> Dict[int, Dict[str, int]]: """Get the operation counts. Returns: The counts of each operation performed per iteration. """ return self._operation_counts @property def n_input_qubits(self) -> int: """Getter of n_input_qubits Returns: The number of qubits used to represent the input. """ return self._n_input_qubits @property def n_output_qubits(self) -> int: """Getter of n_output_qubits Returns: The number of qubits used to represent the output. """ return self._n_output_qubits @property def intermediate_fval(self) -> float: """Getter of the intermediate fval Returns: The intermediate value of fval before interpret. """ return self._intermediate_fval @property def threshold(self) -> float: """Getter of the threshold of Grover algorithm. Returns: The threshold of Grover algorithm. """ return self._threshold @property def raw_samples(self) -> Optional[List[SolutionSample]]: """Returns the list of raw solution samples of ``GroverOptimizer``. Returns: The list of raw solution samples of ``GroverOptimizer``. """ return self._raw_samples