Real Variance-Based Variational Quantum Eigensolver for Non-Hermitian Matrices

Quantum Physics [Submitted on 30 Mar 2026] Real Variance-Based Variational Quantum Eigensolver for Non-Hermitian Matrices Durgesh Pandey, Ankit Kumar Das, P. Arumugam Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the Variational Quantum Eigensolver (VQE), are designed for Hermitian operators and are ineffective in recovering correct eigenvalues for non-Hermitian matrices. We present a systematic formulation based on a Real Variance-based Variational Quantum Eigensolver (RVVQE) for non-Hermitian operators. A correct cost function that guarantees convergence to the true eigenstates is identified. Our implementation utilizes Hermitian measurements only, rendering the algorithm easily deliverable. The performance and scalability of the proposed algorithm on a hierarchy of dense non-Hermitian matrices of increasing dimension are demonstrated with numerical results and computational metrics. Comments: 7 pages, 6 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.28892 [quant-ph]   (or arXiv:2603.28892v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.28892 Focus to learn more Submission history From: P. Arumugam [view email] [v1] Mon, 30 Mar 2026 18:16:42 UTC (5,453 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)