2023-09-30T08:59:47Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002250642023-04-27T10:00:04Z01164:10193:11168:11169
Sequential Quantum Optimizer of Parameterized Quantum Circuits for Generalized Eigenvalue ProblemsSequential Quantum Optimizer of Parameterized Quantum Circuits for Generalized Eigenvalue Problemsenghttp://id.nii.ac.jp/1001/00224955/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=225064&item_no=1&attribute_id=1&file_no=1Copyright (c) 2023 by the Information Processing Society of JapanToyota Central R&D Labs., Inc.／Quantum Computing Center, Keio UniversityQuantum Computing Center, Keio UniversityIBM Quantum, IBM Japan／Quantum Computing Center, Keio University／Department of Computer Science, The University of TokyoToyota Central R&D Labs., Inc.／Quantum Computing Center, Keio UniversityDepartment of Applied Physics and Physico-Informatics, Keio UniversityResearch Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST)／Quantum Computing Center, Keio UniversityQuantum Computing Center, Keio UniversityQuantum Computing Center, Keio University／Department of Applied Physics and Physico-Informatics, Keio UniversityYuki, SatoHiroshi, C. WatanabeRudy, RaymondRuho, KondoKaito, WadaKatsuhiro, EndoMichihiko, SugawaraNaoki, YamamotoGeneralized eigenvalue problems (GEPs) play an important role in a variety of fields, including engineering and machine learning. Many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the critical problems in handling GEPs is that memory usage and computational complexity explode as the system of interest grows. This paper aims to extend sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms which iterate the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the problem of finding the minimum eigenvalue of a GEP as the minimization problem of the fractional form of the expectations of two Hermitians. We then showed that the minimization problem could be analytically solved for a single-qubit gate by solving a GEP of a 4 × 4 matrix. Second, we show that a system of linear equations (SLE) characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to essential engineering problems formulated with the finite element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.Generalized eigenvalue problems (GEPs) play an important role in a variety of fields, including engineering and machine learning. Many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the critical problems in handling GEPs is that memory usage and computational complexity explode as the system of interest grows. This paper aims to extend sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms which iterate the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the problem of finding the minimum eigenvalue of a GEP as the minimization problem of the fractional form of the expectations of two Hermitians. We then showed that the minimization problem could be analytically solved for a single-qubit gate by solving a GEP of a 4 × 4 matrix. Second, we show that a system of linear equations (SLE) characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to essential engineering problems formulated with the finite element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.AA12894105研究報告量子ソフトウェア（QS）2023-QS-828172023-03-062435-64922023-03-01