http://swrc.ontoware.org/ontology#TechnicalReport
Sequential Quantum Optimizer of Parameterized Quantum Circuits for Generalized Eigenvalue Problems
en
Toyota Central R&D Labs., Inc.／Quantum Computing Center, Keio University
Quantum Computing Center, Keio University
IBM Quantum, IBM Japan／Quantum Computing Center, Keio University／Department of Computer Science, The University of Tokyo
Toyota Central R&D Labs., Inc.／Quantum Computing Center, Keio University
Department of Applied Physics and Physico-Informatics, Keio University
Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST)／Quantum Computing Center, Keio University
Quantum Computing Center, Keio University
Quantum Computing Center, Keio University／Department of Applied Physics and Physico-Informatics, Keio University
Yuki Sato
Hiroshi C. Watanabe
Rudy Raymond
Ruho Kondo
Kaito Wada
Katsuhiro Endo
Michihiko Sugawara
Naoki Yamamoto
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.
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-8
28
1-7
2023-03-06
2435-6492