PVQD

class qiskit.algorithms.PVQD(fidelity, ansatz, initial_parameters, estimator=None, optimizer=None, num_timesteps=None, evolution=None, use_parameter_shift=True, initial_guess=None)

Bases: RealTimeEvolver

The projected Variational Quantum Dynamics (p-VQD) Algorithm.

In each timestep, this algorithm computes the next state with a Trotter formula (specified by the evolution argument) and projects the timestep onto a variational form (ansatz). The projection is determined by maximizing the fidelity of the Trotter-evolved state and the ansatz, using a classical optimization routine. See Ref. [1] for details.

The following attributes can be set via the initializer but can also be read and updated once the PVQD object has been constructed.

ansatz

initial_parameters

optimizer

num_timesteps

evolution

use_parameter_shift

initial_guess

Example

This snippet computes the real time evolution of a quantum Ising model on two neighboring sites and keeps track of the magnetization.

import numpy as np
 
from qiskit.algorithms.state_fidelities import ComputeUncompute
from qiskit.algorithms.time_evolvers import TimeEvolutionProblem, PVQD
from qiskit.primitives import Estimator, Sampler
from qiskit.circuit.library import EfficientSU2
from qiskit.quantum_info import SparsePauliOp, Pauli
from qiskit.algorithms.optimizers import L_BFGS_B
 
sampler = Sampler()
fidelity = ComputeUncompute(sampler)
estimator = Estimator()
hamiltonian = 0.1 * SparsePauliOp(["ZZ", "IX", "XI"])
observable = Pauli("ZZ")
ansatz = EfficientSU2(2, reps=1)
initial_parameters = np.zeros(ansatz.num_parameters)
 
time = 1
optimizer = L_BFGS_B()
 
# setup the algorithm
pvqd = PVQD(
    fidelity,
    ansatz,
    initial_parameters,
    estimator,
    num_timesteps=100,
    optimizer=optimizer,
)
 
# specify the evolution problem
problem = TimeEvolutionProblem(
    hamiltonian, time, aux_operators=[hamiltonian, observable]
)
 
# and evolve!
result = pvqd.evolve(problem)

References

[1] Stefano Barison, Filippo Vicentini, and Giuseppe Carleo (2021), An efficient

quantum algorithm for the time evolution of parameterized circuits, Quantum 5, 512.

Parameters

• fidelity (BaseStateFidelity) – A fidelity primitive used by the algorithm.
• ansatz (QuantumCircuit) – A parameterized circuit preparing the variational ansatz to model the time evolved quantum state.
• initial_parameters (np.ndarray) – The initial parameters for the ansatz. Together with the ansatz, these define the initial state of the time evolution.
• estimator (BaseEstimator | None) – An estimator primitive used for calculating expected values of auxiliary operators (if provided via the problem).
• optimizer (Optimizer |Minimizer | None) – The classical optimizers used to minimize the overlap between Trotterization and ansatz. Can be either a Optimizer or a callable using the Minimizer protocol. This argument is optional since it is not required for get_loss(), but it has to be set before evolve() is called.
• num_timesteps (int | None) – The number of time steps. If None it will be set such that the timestep is close to 0.01.
• evolution (EvolutionSynthesis | None) – The evolution synthesis to use for the construction of the Trotter step. Defaults to first-order Lie-Trotter decomposition, see also evolution for different options.
• use_parameter_shift (bool) – If True, use the parameter shift rule to compute gradients. If False, the optimizer will not be passed a gradient callable. In that case, Qiskit optimizers will use a finite difference rule to approximate the gradients.
• initial_guess (np.ndarray | None) – The initial guess for the first VQE optimization. Afterwards the previous iteration result is used as initial guess. If None, this is set to a random vector with elements in the interval $[-0.01, 0.01]$.

Methods

evolve

get_loss

step