Measurement Schemes for Quantum Linear Equation Solvers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912280974721024 |
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| author | Patterson, Andrew Lapworth, Leigh |
| author_facet | Patterson, Andrew Lapworth, Leigh |
| contents | Solving Computational Fluid Dynamics (CFD) problems requires the inversion of a linear system of equations, which can be done using a quantum algorithm for matrix inversion arxiv:1806.01838. However, the number of shots required to measure the output of the system can be prohibitive and remove any advantage obtained by quantum computing. In this work we propose a scheme for measuring the output of QSVT matrix inversion algorithms specifically for the CFD use case. We use a Quantum Signal Processing (QSP) based amplitude estimation algorithm arxiv:2207.08628 and show how it can be combined with the QSVT matrix inversion algorithm. We perform a detailed resource estimation of the amount of computational resources required for a single iteration of amplitude estimation, and compare the costs of amplitude estimation with the cost of not doing amplitude estimation and measuring the whole wavefunction. We also propose a measurement scheme to reduce the number of amplitudes measured in the CFD example by focusing on large amplitudes only. We simulate the whole CFD loop, finding that thus measuring only a small number of the total amplitudes in the output vector still results in an acceptable level of overall error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measurement Schemes for Quantum Linear Equation Solvers Patterson, Andrew Lapworth, Leigh Quantum Physics Solving Computational Fluid Dynamics (CFD) problems requires the inversion of a linear system of equations, which can be done using a quantum algorithm for matrix inversion arxiv:1806.01838. However, the number of shots required to measure the output of the system can be prohibitive and remove any advantage obtained by quantum computing. In this work we propose a scheme for measuring the output of QSVT matrix inversion algorithms specifically for the CFD use case. We use a Quantum Signal Processing (QSP) based amplitude estimation algorithm arxiv:2207.08628 and show how it can be combined with the QSVT matrix inversion algorithm. We perform a detailed resource estimation of the amount of computational resources required for a single iteration of amplitude estimation, and compare the costs of amplitude estimation with the cost of not doing amplitude estimation and measuring the whole wavefunction. We also propose a measurement scheme to reduce the number of amplitudes measured in the CFD example by focusing on large amplitudes only. We simulate the whole CFD loop, finding that thus measuring only a small number of the total amplitudes in the output vector still results in an acceptable level of overall error. |
| title | Measurement Schemes for Quantum Linear Equation Solvers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.00723 |