Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914871748067328 |
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| author | Brearley, Peter Laizet, Sylvain |
| author_facet | Brearley, Peter Laizet, Sylvain |
| contents | A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. Here, this is extended to industrially relevant, multi-dimensional flows with realistic boundary conditions and arbitrary finite difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator and the inverse of the allowable error. Statevector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09784 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation Brearley, Peter Laizet, Sylvain Quantum Physics A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. Here, this is extended to industrially relevant, multi-dimensional flows with realistic boundary conditions and arbitrary finite difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator and the inverse of the allowable error. Statevector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach. |
| title | Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.09784 |