2022/08/31 by Koichi Miyamoto, Miyamoto, Koichi, Hiroshi Ueda +1 · 2 citations
Computer Science · #Computational Physics and Python Applications #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2208.14623
openalex publication_date 2022/08/31 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
There are quantum algorithms for finding a function f satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the number d of the variables of f is large. In general, however, these algorithms output the quantum state which encodes f in the amplitudes, and reading out the values of f as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this study, we propose a general method for this function readout task. Based on the function approximation by a combination of tensor network and orthogonal function expansion, we present a quantum circuit and its optimization procedure to obtain an approximating function of f that has a polynomial number of degrees of freedom with respect to d and is efficiently evaluable on a classical computer. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.