---
title: PVQD (v0.46)
description: API reference for qiskit.algorithms.PVQD in qiskit v0.46
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/0.46/qiskit.algorithms.PVQD
---

# 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)`

[GitHub](https://github.com/qiskit/qiskit/tree/stable/0.46/qiskit/algorithms/time_evolvers/pvqd/pvqd.py)

Bases: [`RealTimeEvolver`](/docs/api/qiskit/0.46/qiskit.algorithms.RealTimeEvolver "qiskit.algorithms.time_evolvers.real_time_evolver.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

The parameterized circuit representing the time-evolved state.

**Type**

[QuantumCircuit](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")

### 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**

Optional\[Union\[[Optimizer](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer"), [Minimizer](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer")]]

### 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](https://docs.python.org/3/library/functions.html#int)]

### evolution

The method to perform the Trotter step. Defaults to first-order Lie-Trotter evolution.

**Type**

Optional\[[EvolutionSynthesis](/docs/api/qiskit/0.46/qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.EvolutionSynthesis")]

### use\_parameter\_shift

If True, use the parameter shift rule for loss function gradients (if the ansatz supports).

**Type**

[bool](https://docs.python.org/3/library/functions.html#bool)

### initial\_guess

The starting point for the first classical optimization run, at time 0. Defaults to random values in $[-0.01, 0.01]$.

**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.

```python
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](https://quantum-journal.org/papers/q-2021-07-28-512/).

**Parameters**

- **fidelity** ([*BaseStateFidelity*](/docs/api/qiskit/0.46/qiskit.algorithms.state_fidelities.BaseStateFidelity "qiskit.algorithms.state_fidelities.BaseStateFidelity")) – A fidelity primitive used by the algorithm.
- **ansatz** ([*QuantumCircuit*](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.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*](/docs/api/qiskit/0.46/qiskit.primitives.BaseEstimator "qiskit.primitives.BaseEstimator") *| None*) – An estimator primitive used for calculating expected values of auxiliary operators (if provided via the problem).
- **optimizer** ([*Optimizer*](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer")  *|*[*Minimizer*](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") *| None*) – The classical optimizers used to minimize the overlap between Trotterization and ansatz. Can be either a [`Optimizer`](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") or a callable using the [`Minimizer`](/docs/api/qiskit/0.46/qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") protocol. This argument is optional since it is not required for [`get_loss()`](#qiskit.algorithms.PVQD.get_loss "qiskit.algorithms.PVQD.get_loss"), but it has to be set before [`evolve()`](#qiskit.algorithms.PVQD.evolve "qiskit.algorithms.PVQD.evolve") is called.
- **num\_timesteps** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – The number of time steps. If `None` it will be set such that the timestep is close to 0.01.
- **evolution** ([*EvolutionSynthesis*](/docs/api/qiskit/0.46/qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.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*](https://docs.python.org/3/library/functions.html#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

`evolve(evolution_problem)`

Perform real time evolution $\exp(-i t H)|\Psi\rangle$.

Evolves an initial state $|\Psi\rangle$ for a time $t$ under a Hamiltonian $H$, as provided in the `evolution_problem`.

**Parameters**

**evolution\_problem** ([*TimeEvolutionProblem*](/docs/api/qiskit/0.46/qiskit.algorithms.TimeEvolutionProblem "qiskit.algorithms.time_evolvers.time_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**](https://docs.python.org/3/library/exceptions.html#ValueError) – If `aux_operators` provided in the time evolution problem but no estimator provided to the algorithm.
- [**NotImplementedError**](https://docs.python.org/3/library/exceptions.html#NotImplementedError) – If the evolution problem contains an initial state.

**Return type**

[*TimeEvolutionResult*](/docs/api/qiskit/0.46/qiskit.algorithms.TimeEvolutionResult "qiskit.algorithms.time_evolvers.time_evolution_result.TimeEvolutionResult")

### 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*](/docs/api/qiskit/0.46/qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – The Hamiltonian under which to evolve.
- **ansatz** ([*QuantumCircuit*](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
- **dt** ([*float*](https://docs.python.org/3/library/functions.html#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](https://docs.python.org/3/library/stdtypes.html#tuple)\[Callable\[\[np.ndarray], [float](https://docs.python.org/3/library/functions.html#float)], Callable\[\[np.ndarray], np.ndarray]] | None

### step

`step(hamiltonian, ansatz, theta, dt, initial_guess)`

Perform a single time step.

**Parameters**

- **hamiltonian** (*BaseOperator |* [*PauliSumOp*](/docs/api/qiskit/0.46/qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – The Hamiltonian under which to evolve.
- **ansatz** ([*QuantumCircuit*](/docs/api/qiskit/0.46/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
- **theta** (*np.ndarray*) – The current parameters.
- **dt** ([*float*](https://docs.python.org/3/library/functions.html#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 $[-0.01, 0.01]$.

**Returns**

A tuple consisting of the next parameters and the fidelity of the optimization.

**Return type**

[tuple](https://docs.python.org/3/library/stdtypes.html#tuple)\[np.ndarray, [float](https://docs.python.org/3/library/functions.html#float)]