When is randomization advantageous in quantum simulation?

Quantum Physics [Submitted on 8 Apr 2026] When is randomization advantageous in quantum simulation? Francesco Paganelli, Michele Grossi, Andrea Giachero, Thomas E. O'Brien, Oriel Kiss We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller contributions are sampled stochastically. Crucially, we analyze how stochastic and approximation errors propagate through block-encoding and QSVT procedures. To benchmark this approach, we construct ensembles of random Hamiltonians with controlled coefficient dispersion, locality, and number of terms, designed to favor randomization, and therefore providing an upper bound on its practical advantage. For Hamiltonians with many terms and highly inhomogeneous coefficient distributions, randomized methods reduce gate counts by up to an order of magnitude. However, this advantage is confined to moderate-precision regimes: as the target error decreases, deterministic methods become more efficient, with a crossover near \varepsilon \sim 10^{-3}. Although this regime partially overlaps with quantum chemistry Hamiltonians, realistic systems exhibit additional structure, such as commutation patterns, not captured by our model, which are expected to further favor deterministic approaches. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.07448 [quant-ph]   (or arXiv:2604.07448v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.07448 Focus to learn more Submission history From: Francesco Paganelli [view email] [v1] Wed, 8 Apr 2026 18:00:04 UTC (1,744 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)