qcr:2604.02203.1

Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation

Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often intractable within a reasonable computation time, even when using supercomputers. To overcome the inherent limit of classical computing, we present a variational quantum algorithm for solving the Poisson equation that can be implemented in noisy intermediate-scale quantum devices. The proposed method defines the total potential energy of the Poisson equation as a Hamiltonian, which is decomposed into a linear combination of Pauli operators and simple observables. The expectation value of the Hamiltonian is then minimized with respect to a parameterized quantum state. Because the number of decomposed terms is independent of the size of the problem, this method requires relatively few quantum measurements. Numerical experiments demonstrate the faster computing speed of this method compared with classical computing methods and a previous variational quantum approach. We believe that our approach brings quantum computer-aided techniques closer to future applications in engineering developments. Code is available at https://github.com/ToyotaCRDL/VQAPoisson.

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Circuit-based

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ToyotaCRDL/VQAPoisson

README.md

Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation

This codes solves the one-dimensional Poisson equation based on the variational quantum algorithm.

Requirement

Software	Version
python	3.7.4
qiskit	0.23.6
qiskit-aer	0.7.5
qiskit-aqua	0.8.2
numpy	1.19.1
scipy	1.6.1

To run jupyter notebook,

Software	Version
matplotlib	3.4.2
tqdm	4.60.0

Usage

See sample.ipynb as a sample code.

from vqa_poisson import VQAforPoisson

num_qubits = ... # int
num_layers = ... # int
bc = ... # str
oracle_f = ... # qiskit.QuantumCircuit
qins = ... # qiskit.aqua.QuantumInstance
vqa = VQAforPoisson(num_qubits, num_layers, bc, oracle_f=oracle_f, qinstance=qins)
x0 = ... # numpy.ndarray
res = vqa.minimize(x0)

Citing the library

If you find it useful to use this module in your research, please cite the following paper.

Yuki Sato, Ruho Kondo, Satoshi Koide, Hideki Takamatsu, and Nobuyuki Imoto, Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation, Physical Review A, 104: 052409, 2021.

In bibtex format:

@article{sato2021vqa,
  author  = {Sato, Yuki and Kondo, Ruho and Koide, Satoshi and Takamatsu, Hideki and Imoto, Nobuyuki},
  title   = {Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation},
  journal = {Physical Review A},
  year    = {2021},
  volume  = {104},
  issue   = {5},
  pages   = {052409},
}

License

This project is licensed under the Apache License Version 2.0 - see the LICENSE.txt file for details

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