High order schemes for solving partial differential equations on a quantum computer
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910764718096384 |
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| author | Arseniev, Boris Guskov, Dmitry Sengupta, Richik Zacharov, Igor |
| author_facet | Arseniev, Boris Guskov, Dmitry Sengupta, Richik Zacharov, Igor |
| contents | We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for decomposing $d$-band diagonal matrices into Pauli strings that are grouped into mutually commuting sets.
Using numerical simulations of the one-dimensional wave equation, we show that higher-order methods can reduce the number of qubits necessary for discretization, similar to the classical case, although they do not decrease the number of Trotter steps needed to preserve solution accuracy. This result has important consequences for the practical application of quantum algorithms based on Hamiltonian evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High order schemes for solving partial differential equations on a quantum computer Arseniev, Boris Guskov, Dmitry Sengupta, Richik Zacharov, Igor Quantum Physics Emerging Technologies We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for decomposing $d$-band diagonal matrices into Pauli strings that are grouped into mutually commuting sets. Using numerical simulations of the one-dimensional wave equation, we show that higher-order methods can reduce the number of qubits necessary for discretization, similar to the classical case, although they do not decrease the number of Trotter steps needed to preserve solution accuracy. This result has important consequences for the practical application of quantum algorithms based on Hamiltonian evolution. |
| title | High order schemes for solving partial differential equations on a quantum computer |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2412.19232 |