Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion

Abstract There are quantum algorithms for finding a function f satisfying set of conditions, such as solving partial differential equations, and these achieve exponential speedup compared to existing classical methods, especially when the number d variables is large. In general, however, output state which encodes in amplitudes, reading out values data from can be so time-consuming that ruined. this study, we propose general method readout task. Based on approximation by combination tensor network orthogonal expansion, present circuit its optimization procedure obtain an approximating has polynomial degrees freedom with respect efficiently evaluable computer. We also conducted numerical experiment approximate finance-motivated demonstrate our works.