75 lines
5.0 KiB
Plaintext
75 lines
5.0 KiB
Plaintext
---
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title: variational
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description: API reference for qiskit.algorithms.time_evolvers.variational
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in_page_toc_min_heading_level: 2
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python_api_type: module
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python_api_name: qiskit.algorithms.time_evolvers.variational
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---
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<span id="qiskit-algorithms-time-evolvers-variational" />
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# qiskit.algorithms.time\_evolvers.variational
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## Variational Quantum Time Evolutions
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<span id="module-qiskit.algorithms.time_evolvers.variational" />
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`qiskit.algorithms.time_evolvers.variational`
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Algorithms for performing Variational Quantum Time Evolution of quantum states, which can be tailored to near-term devices. `VarQTE` base class exposes an interface, compliant with the Quantum Time Evolution Framework in Qiskit Terra, that is implemented by [`VarQRTE`](qiskit.algorithms.VarQRTE "qiskit.algorithms.VarQRTE") and [`VarQITE`](qiskit.algorithms.VarQITE "qiskit.algorithms.VarQITE") classes for real and imaginary time evolution respectively. The variational approach is taken according to a variational principle chosen by a user.
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**Example**
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```python
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import numpy as np
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from qiskit.algorithms import TimeEvolutionProblem, VarQITE
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from qiskit.algorithms.time_evolvers.variational import ImaginaryMcLachlanPrinciple
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from qiskit.circuit.library import EfficientSU2
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from qiskit.quantum_info import SparsePauliOp
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observable = SparsePauliOp.from_list(
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[
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("II", 0.2252),
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("ZZ", 0.5716),
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("IZ", 0.3435),
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("ZI", -0.4347),
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("YY", 0.091),
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("XX", 0.091),
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]
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)
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ansatz = EfficientSU2(observable.num_qubits, reps=1)
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init_param_values = np.zeros(len(ansatz.parameters))
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for i in range(len(ansatz.parameters)):
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init_param_values[i] = np.pi / 2
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var_principle = ImaginaryMcLachlanPrinciple()
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time = 1
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evolution_problem = TimeEvolutionProblem(observable, time)
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var_qite = VarQITE(ansatz, var_principle, init_param_values)
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evolution_result = var_qite.evolve(evolution_problem)
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```
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### Variational Principles
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With variational principles we can project time evolution of a quantum state onto the parameters of a model, in our case a variational quantum circuit.
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They can be divided into two categories: Variational Quantum \_Real\_ Time Evolution, which evolves the variational ansatz under the standard Schroediger equation and Variational Quantum \_Imaginary\_ Time Evolution, which evolves under the normalized Wick-rotated Schroedinger equation.
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| | |
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| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------- |
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| [`VariationalPrinciple`](qiskit.algorithms.time_evolvers.variational.VariationalPrinciple "qiskit.algorithms.time_evolvers.variational.VariationalPrinciple")(qgt, gradient) | A Variational Principle class. |
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| [`RealVariationalPrinciple`](qiskit.algorithms.time_evolvers.variational.RealVariationalPrinciple "qiskit.algorithms.time_evolvers.variational.RealVariationalPrinciple")(qgt, gradient) | Class for a Real Variational Principle. |
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| [`ImaginaryVariationalPrinciple`](qiskit.algorithms.time_evolvers.variational.ImaginaryVariationalPrinciple "qiskit.algorithms.time_evolvers.variational.ImaginaryVariationalPrinciple")(qgt, gradient) | Abstract class for an Imaginary Variational Principle. |
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| [`RealMcLachlanPrinciple`](qiskit.algorithms.time_evolvers.variational.RealMcLachlanPrinciple "qiskit.algorithms.time_evolvers.variational.RealMcLachlanPrinciple")(\[qgt, gradient]) | Class for a Real McLachlan's Variational Principle. |
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| [`ImaginaryMcLachlanPrinciple`](qiskit.algorithms.time_evolvers.variational.ImaginaryMcLachlanPrinciple "qiskit.algorithms.time_evolvers.variational.ImaginaryMcLachlanPrinciple")(\[qgt, gradient]) | Class for an Imaginary McLachlan's Variational Principle. |
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### ODE solvers
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ODE solvers that implement the SciPy ODE Solver interface. The Forward Euler Solver is a preferred choice in the presence of noise. One might also use solvers provided by SciPy directly, e.g. RK45.
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| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------- |
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| [`ForwardEulerSolver`](qiskit.algorithms.time_evolvers.variational.ForwardEulerSolver "qiskit.algorithms.time_evolvers.variational.ForwardEulerSolver")(function, t0, y0, t\_bound) | Forward Euler ODE solver. |
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