Year: 2026
Type: article
Abstract: Stability is a fundamental property of dynamical systems, and Lyapunov theory provides a rigorous link between stability and eigenvalue distribution. By computing eigenvalues, quantum algorithms may offer potential advantages for evaluating the stability of high-dimensional systems under appropriate assumptions regarding data access and quantum resource requirements. In this work, we introduce a quantum algorithm based on the quantum singular value transformation (QSVT) to efficiently resolve the complex eigenspectrum of non-Hermitian matrices and determine asymptotic stability. By employing block encoding and QSVT techniques, we implement a polynomial transformation to approximate the singular value threshold problem, enabling the localization of eigenvalues with positive real parts under appropriate requirements regarding block encoding efficiency, matrix conditioning, state overlap, and precision. We validate the method numerically on a one-dimensional non-Hermitian spin-1/2 chain with local gain and loss, demonstrating accurate detection of unstable and stable cases, which is consistent with the results obtained by exact diagonalization. These results show that our quantum algorithm is a reliable and powerful tool for stability analysis and spectral characterization of high-dimensional dynamical systems.
Source: New Journal of Physics
Authors: Mingwu He, Xiao-Ming Zhang
Institution: South China Normal University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
Award: G60897888
OpenAlex ID: W7223366598