Towards End-to-End Quantum Estimation of Non-Hermitian Pseudospectra

Quantum Physics [Submitted on 17 Mar 2026] Towards End-to-End Quantum Estimation of Non-Hermitian Pseudospectra Gengzhi Yang, Jiaqi Leng, Xiaodi Wu, Lin Lin Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially small \epsilon, we show that deciding whether a point z\in\mathbb{C} is \epsilon-close to the spectrum is PSPACE-hard for 5-local operators, whereas deciding whether z lies in the \epsilon-pseudospectrum is QMA-complete for 4-local operators. This identifies pseudospectrum membership as a natural computational target. We then present a concrete end-to-end quantum framework for deciding pseudospectrum membership, which combines a singular-value estimation step with a dissipative state preparation algorithm. Our Quantum Singular-value Gaussian-filtered Search (QSIGS) combines quantum singular value transformation (QSVT) with classical post-processing to achieve Heisenberg-limited query scaling for singular-value estimation. To prepare suitable input states, we introduce an algorithmic Lindbladian protocol for approximate ground right singular vectors and prove its effectiveness for the Hatano--Nelson model. Finally, we demonstrate the full pipeline on a trapped-ion quantum computer and distinguish points inside and outside the target pseudospectrum near the exceptional point of a minimal non-Hermitian qubit model. Subjects: Quantum Physics (quant-ph); Numerical Analysis (math.NA) Cite as: arXiv:2603.16214 [quant-ph]   (or arXiv:2603.16214v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.16214 Focus to learn more Submission history From: Gengzhi Yang [view email] [v1] Tue, 17 Mar 2026 07:44:04 UTC (630 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.NA math math.NA 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?)