2026-06-06T14:01:22Z https://ipsj.ixsq.nii.ac.jp/oai

oai:ipsj.ixsq.nii.ac.jp:00220408 2025-01-19T14:35:06Z 1164:10193:10905:11012

Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion Koichi, Miyamoto Hiroshi, Ueda Koichi, Miyamoto Hiroshi, Ueda There are some quantum algorithms on problems to find the functions satisfying the given conditions, such as solving partial differential equations, and they claim the exponential quantum speedup compared to the classical methods. However, they in general output the quantum state in which the solution function is encoded in the amplitudes, and reading out the function values as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this paper, we propose a general method to such a function readout task. We approximate the function by orthogonal function expansion. Besides, in order to avoid the exponential increase of the parameter number for the high-dimensional function, we use the tensor network that approximately reproduces the expansion coefficients as a high-order tensor. We present the quantum circuit that encodes such a tensor network-based function approximation and the procedure to optimize the circuit and obtain the approximating function. We also conduct the numerical experiment to approximate some finance-motivated function and observe that our method works. There are some quantum algorithms on problems to find the functions satisfying the given conditions, such as solving partial differential equations, and they claim the exponential quantum speedup compared to the classical methods. However, they in general output the quantum state in which the solution function is encoded in the amplitudes, and reading out the function values as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this paper, we propose a general method to such a function readout task. We approximate the function by orthogonal function expansion. Besides, in order to avoid the exponential increase of the parameter number for the high-dimensional function, we use the tensor network that approximately reproduces the expansion coefficients as a high-order tensor. We present the quantum circuit that encodes such a tensor network-based function approximation and the procedure to optimize the circuit and obtain the approximating function. We also conduct the numerical experiment to approximate some finance-motivated function and observe that our method works. 情報処理学会 2022-10-20 eng technical report https://ipsj.ixsq.nii.ac.jp/records/220408 2435-6492 AA12894105 研究報告量子ソフトウェア（QS） 2022-QS-7 4 1 10 https://ipsj.ixsq.nii.ac.jp/record/220408/files/IPSJ-QS22007004.pdf application/pdf 848.0 kB 2024-10-20