Compact quantum algorithms that can potentially maintain quantum advantage for solving time-dependent differential equations
- URL: http://arxiv.org/abs/2405.09767v1
- Date: Thu, 16 May 2024 02:14:58 GMT
- Title: Compact quantum algorithms that can potentially maintain quantum advantage for solving time-dependent differential equations
- Authors: Sachin S. Bharadwaj, Katepalli R. Sreenivasan,
- Abstract summary: We present algorithms for solving time-dependent PDEs governing fluid flow problems.
We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems.
These algorithms lead to low-depth quantum circuits that protect quantum advantage.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs governing fluid flow problems. We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems, and generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations. These algorithms lead to low-depth quantum circuits that protect quantum advantage, with the best-case asymptotic complexities that are near-optimal. We demonstrate the performance of the algorithms by conducting: (a) ideal state-vector simulations using an in-house, high performance, quantum simulator called $\textit{QFlowS}$; (b) experiments on a real quantum device (IBM Cairo); and (c) noisy simulations using Qiskit Aer. We also provide device specifications such as error-rates (noise) and state sampling (measurement) to accurately perform convergent flow simulations on noisy devices.
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