Active Sampling Sample-based Quantum Diagonalization from Finite-Shot Measurements

Quantum Physics [Submitted on 13 Mar 2026] Active Sampling Sample-based Quantum Diagonalization from Finite-Shot Measurements Rinka Miura Near-term quantum devices provide only finite-shot measurements and prepare imperfect, contaminated states. This motivates algorithms that convert samples into reliable low-energy estimates without full tomography or exhaustive measurements. We propose Active Sampling Sample-based Quantum Diagonalization (AS-SQD), framing SQD as an active learning problem: given measured bitstrings, which additional basis states should be included to efficiently recover the ground-state energy? SQD restricts the Hamiltonian to a selected set of basis states and classically diagonalizes the restricted matrix. However, naive SQD using only sampled states suffers from bias under finite-shot sampling and excited-state contamination, while blind random expansion is inefficient as system size grows. We introduce a perturbation-theoretic acquisition function based on Epstein--Nesbet second-order energy corrections to rank candidate basis states connected to the current subspace. At each iteration, AS-SQD diagonalizes the restricted Hamiltonian, generates connected candidates, and adds the most valuable ones according to this score. We evaluate AS-SQD on disordered Heisenberg and Transverse-Field Ising (TFIM) spin chains up to 16 qubits under a preparation model mixing 80\% ground state and 20\% first excited state. Furthermore, we validate its robustness against real-world state preparation and measurement (SPAM) errors using physical samples from an IBM Quantum processor. Across simulated and hardware evaluations, AS-SQD consistently achieves substantially lower absolute energy errors than standard SQD and random expansion. Detailed ablation studies demonstrate that physics-guided basis acquisition effectively concentrates computation on energetically relevant directions, bypassing exponential combinatorial bottlenecks. Comments: 7 pages, 5 figures Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2603.13536 [quant-ph]   (or arXiv:2603.13536v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.13536 Focus to learn more Journal reference: IEEE International Conference on Quantum Communications, Networking, and Computing (QCNC 2026) Submission history From: Rinka Miura [view email] [v1] Fri, 13 Mar 2026 19:17:33 UTC (491 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.LG 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?)