2021/12/28 by Jin‐Min Liang, Jin-Min Liang, Shu-Qian Shen +3
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Eigenvalues and eigenvectors #Mathematics #Matrix pencil #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Qubit #Rayleigh quotient #quant-ph
paper · pdf · doi:10.1007/s11128-021-03370-z
published as Quantum Inf Process 21, 23 (2022)
openalex publication_date 2021/12/28 · arxiv created 2022/03/06 · arxiv updated 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, A|ψ⟩=λB|ψ⟩, by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained eigenvectors with respect to the weighting matrix B on the Rayleigh-quotient. Furthermore, both the values and derivatives of the loss functions can be calculated on near-term quantum devices with shallow quantum circuit. Finally, we propose a full quantum generalized eigensolver (FQGE) to calculate the minimal generalized eigenvalue with quantum gradient descent algorithm. As a demonstration of the principle, we numerically implement our algorithms to conduct a 2-qubit simulation and successfully find the generalized eigenvalues of the matrix pencil (A, B). The numerically experimental result indicates that FQGE is robust under Gaussian noise.