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

• URL: http://arxiv.org/abs/2208.14623v2
• Date: Thu, 1 Jun 2023 09:05:39 GMT
• Title: Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
• Authors: Koichi Miyamoto, Hiroshi Ueda
• Abstract summary: We present a quantum circuit and its optimization procedure to obtain an approximating function of $f$ that has a number of degrees of freedom with respect to $d$. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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