Quantum algorithm for partial differential equations of nonconservative systems with spatially varying parameters

This repository provides codes to reproduce results of the paper:

Yuki Sato, Hiroyuki Tezuka, Ruho Kondo, and Naoki Yamamoto,
Quantum algorithm for partial differential equations of nonconservative systems with spatially varying parameters,
Physical Review Applied 23, 014063, 2025.

Requirement

Software	Version
python	3.10
tqdm	4.66
qiskit	1.0
qiskit-aer	0.13

Contents

Section IV A, Acoustic simulation: Section4A-waveEq.ipynb

Section IV B, LCU coefficient: Section4B-LCU.ipynb

Section IV B, Heat simulation: Section4B-heatEq.ipynb

Note: codes for Hamiltonian simulation are based on those in our another repository

Citation

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

Yuki Sato, Hiroyuki Tezuka, Ruho Kondo, and Naoki Yamamoto, Quantum algorithm for partial differential equations of nonconservative systems with spatially varying parameters, Physical Review Applied 23, 014063, 2025.

In bibtex format:

@article{sato2025quantum,
  title={Quantum algorithm for partial differential equations of nonconservative systems with spatially varying parameters},
  author={Sato, Yuki and Tezuka, Hiroyuki and Kondo, Ruho and Yamamoto, Naoki},
  journal={Physical Review Applied},
  volume={23},
  number={1},
  pages={014063},
  year={2025},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevApplied.23.014063},
  url = {https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.23.014063}
}

Since the idea of constructing the quantum circuits for time evolution operators is based on our another paper, please also consider to cite the following paper.

Yuki Sato, Ruho Kondo, Ikko Hamamura, Tamiya Onodera, and Naoki Yamamoto, Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits, Physical Review Research, 6, 033246, 2024.

In bibtex format:

@article{sato2024hamiltonian,
  title={Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits},
  author={Sato, Yuki and Kondo, Ruho and Hamamura, Ikko and Onodera, Tamiya and Yamamoto, Naoki},
  journal={Physical Review Research},
  volume={6},
  number={3},
  pages={033246},
  year={2024},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevResearch.6.033246},
  url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.033246}
}

License

See the LICENSE file for details