Quantum Multi-Resolution Measurement with application to Quantum Linear Solver

• URL: http://arxiv.org/abs/2304.05960v1
• Date: Wed, 12 Apr 2023 16:31:44 GMT
• Title: Quantum Multi-Resolution Measurement with application to Quantum Linear Solver
• Authors: Yoshiyuki Saito, Xinwei Lee, Dongsheng Cai, Nobuyoshi Asai
• Abstract summary: We propose a quantum multi-resolution measurement (QMRM) that gives a solution with an accuracy $epsilon$ in $O(nlog(1/epsilon))$ measurements. The QMRM computational cost with an accuracy $epsilon$ is smaller than $O(n/epsilon2)$. We also propose an algorithm entitled QMRM-QLS (quantum linear solver) for solving a linear system of equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computation consists of a quantum state corresponding to a solution, and measurements with some observables. To obtain a solution with an accuracy $\epsilon$, measurements $O(n/\epsilon^2)$ are required, where $n$ is the size of a problem. The cost of these measurements requires a large computing time for an accurate solution. In this paper, we propose a quantum multi-resolution measurement (QMRM), which is a hybrid quantum-classical algorithm that gives a solution with an accuracy $\epsilon$ in $O(n\log(1/\epsilon))$ measurements using a pair of functions. The QMRM computational cost with an accuracy $\epsilon$ is smaller than $O(n/\epsilon^2)$. We also propose an algorithm entitled QMRM-QLS (quantum linear solver) for solving a linear system of equations using the Harrow-Hassidim-Lloyd (HHL) algorithm as one of the examples. We perform some numerical experiments that QMRM gives solutions to with an accuracy $\epsilon$ in $O(n\log(1/\epsilon))$ measurements.

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