Quantum-Wave-Simulation-with-Sources-and-Loss-Functions

Open-source, 3D Wave equation solver with sources, loss functions, and boundary conditions

> Figure 1: Initialized radially symmetric quantum state. The subplots show vector fields constructed from an initial state in [1,0,0] direction with purely X-, Y-, or Z- vector components.

Overview

Quantum computers show potential for solving wave based forward and inverse problems with major runtime advantages.

We present numerical implementations for educational purposes together with our publication Quantum Wave Simulation with Sources and Loss Functions (11/2024):

Quantum Encoding:

1. A solver for the 2D acoustic wave equation that utilizes a natural quantum encoding.
2. A solver for the 3D Maxwells equations that utilizes a natural quantum encoding.

Loss Functions:

3. An optimally efficient estimation of the energy and the comparison and combination of wave fields encoded as quantum states.
4. An estimation of subspace comparisons, energies, and combinations of wave fields encoded as quantum states.

Sources:

5. An implementation of multiple synchronized pulse sources into the wave equation as a quantum state.
6. An implementation of asynchronous pulse source terms into the wave equation as a quantum state.

Implementation:

7. A full wave quantum wave simulation implementation with sources, boundary conditions, and loss functions using the open-source toolkit Qiskit.
8. A quantum circuit implementation for efficient vector field initialization used in implementing arbitrary source terms.

Enjoy your quantum wave evolution experiments!

Citation

@article{bösch2024quantum,
title={Quantum Wave Simulation with Sources and Loss Functions},
author={Cyrill Bösch, Malte Schade, Giacomo Aloisi, and Andreas Fichtner},
journal={arXiv preprint arXiv:2411.17630},
year={2024},
url={https://arxiv.org/abs/2411.17630}, 
}

Figure 2: Quantum circuit for efficient vector field initialization in 3D. The initial ray is prepared in the quantum register $initial$ with vector components saved in the register $dim$. The registers $grid_{2D}$ (and $grid_{3D}$) are transformed into a state of equal superposition. Afterwards (multi-)controlled RY rotations are applied with decreasing angles, which gives the rotationally symmetric vector field in the combined registers.