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
The parameters of the ansatz at time 0.
Type
np.ndarray
optimizer
The classical optimization routine used to maximize the fidelity of the Trotter step and ansatz.
Type
num_timesteps
The number of timesteps to take. If None, it is automatically selected to achieve a timestep of approximately 0.01.
Type
Optional[int]
evolution
The method to perform the Trotter step. Defaults to first-order Lie-Trotter evolution.
Type
Optional[EvolutionSynthesis]
use_parameter_shift
initial_guess
The starting point for the first classical optimization run, at time 0. Defaults to random values in .
Type
Optional[np.ndarray]
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 theMinimizer
protocol. This argument is optional since it is not required forget_loss()
, but it has to be set beforeevolve()
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 .
Methods
evolve
evolve(evolution_problem)
Perform real time evolution .
Evolves an initial state for a time under a Hamiltonian , as provided in the evolution_problem
.
Parameters
evolution_problem (TimeEvolutionProblem) – The evolution problem containing the hamiltonian, total evolution time and observables to evaluate.
Returns
A result object containing the evolution information and evaluated observables.
Raises
- ValueError – If
aux_operators
provided in the time evolution problem but no estimator provided to the algorithm. - NotImplementedError – If the evolution problem contains an initial state.
Return type
get_loss
get_loss(hamiltonian, ansatz, dt, current_parameters)
Get a function to evaluate the infidelity between Trotter step and ansatz.
Parameters
- hamiltonian (BaseOperator | PauliSumOp) – The Hamiltonian under which to evolve.
- ansatz (QuantumCircuit) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
- dt (float) – The time step.
- current_parameters (np.ndarray) – The current parameters.
Returns
A callable to evaluate the infidelity and, if gradients are supported and required,
a second callable to evaluate the gradient of the infidelity.
Return type
tuple[Callable[[np.ndarray], float], Callable[[np.ndarray], np.ndarray]] | None
step
step(hamiltonian, ansatz, theta, dt, initial_guess)
Perform a single time step.
Parameters
- hamiltonian (BaseOperator | PauliSumOp) – The Hamiltonian under which to evolve.
- ansatz (QuantumCircuit) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
- theta (np.ndarray) – The current parameters.
- dt (float) – The time step.
- initial_guess (np.ndarray) – The initial guess for the classical optimization of the fidelity between the next variational state and the Trotter-evolved last state. If None, this is set to a random vector with elements in the interval .
Returns
A tuple consisting of the next parameters and the fidelity of the optimization.
Return type