تقرير
Compact quantum algorithms that can potentially maintain quantum advantage for solving time-dependent differential equations
| العنوان: | Compact quantum algorithms that can potentially maintain quantum advantage for solving time-dependent differential equations |
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| المؤلفون: | Bharadwaj, Sachin S., Sreenivasan, Katepalli R. |
| سنة النشر: | 2024 |
| المجموعة: | Physics (Other) Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Physics - Applied Physics, Physics - Computational Physics, Physics - Fluid Dynamics |
| الوصف: | 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. Comment: 29 pages, 10 figures, 1 table |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.09767 |
| رقم الأكسشن: | edsarx.2405.09767 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |