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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17630 |
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| _version_ | 1866916597800632320 |
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| author | Bösch, Cyrill Schade, Malte Aloisi, Giacomo Keating, Scott D. Fichtner, Andreas |
| author_facet | Bösch, Cyrill Schade, Malte Aloisi, Giacomo Keating, Scott D. Fichtner, Andreas |
| contents | We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the acoustic wave equation, Maxwell$'$s equations and the elastic wave equation. Our formulation is compatible with standard numerical discretization schemes and allows for the efficient implementation of multiple practically relevant time- and space-dependent sources. Furthermore, we demonstrate that subspace energies can be extracted and wave fields compared through an $l_2$ loss function, achieving optimal precision scaling with the number of samples taken. Additionally, we introduce techniques for incorporating boundary conditions and linear constraints that preserve the anti-Hermitian nature of the equations. Leveraging the Hamiltonian simulation algorithm, our framework achieves a quartic speed-up over classical solvers in 3D simulations, under conditions of sufficiently global measurements and compactly supported sources and initial conditions. This quartic speed-up is optimal for time-domain solutions, as the Hamiltonian of the discretized wave equations has local couplings. In summary, our framework provides a versatile approach for simulating wave equations on quantum computers, offering substantial speed-ups over state-of-the-art classical methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Wave Simulation with Sources and Loss Functions Bösch, Cyrill Schade, Malte Aloisi, Giacomo Keating, Scott D. Fichtner, Andreas Quantum Physics We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the acoustic wave equation, Maxwell$'$s equations and the elastic wave equation. Our formulation is compatible with standard numerical discretization schemes and allows for the efficient implementation of multiple practically relevant time- and space-dependent sources. Furthermore, we demonstrate that subspace energies can be extracted and wave fields compared through an $l_2$ loss function, achieving optimal precision scaling with the number of samples taken. Additionally, we introduce techniques for incorporating boundary conditions and linear constraints that preserve the anti-Hermitian nature of the equations. Leveraging the Hamiltonian simulation algorithm, our framework achieves a quartic speed-up over classical solvers in 3D simulations, under conditions of sufficiently global measurements and compactly supported sources and initial conditions. This quartic speed-up is optimal for time-domain solutions, as the Hamiltonian of the discretized wave equations has local couplings. In summary, our framework provides a versatile approach for simulating wave equations on quantum computers, offering substantial speed-ups over state-of-the-art classical methods. |
| title | Quantum Wave Simulation with Sources and Loss Functions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.17630 |