Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908438660907008 |
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| author | Over, Paul Bengoechea, Sergio Brearley, Peter Laizet, Sylvain Rung, Thomas |
| author_facet | Over, Paul Bengoechea, Sergio Brearley, Peter Laizet, Sylvain Rung, Thomas |
| contents | A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator Over, Paul Bengoechea, Sergio Brearley, Peter Laizet, Sylvain Rung, Thomas Quantum Physics Fluid Dynamics A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings. |
| title | Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator |
| topic | Quantum Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2410.07909 |