Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries

Quantum Physics [Submitted on 23 Mar 2026] Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries Erik J. Gustafson, Henry Lamm We present an extension of the Evolving density matrices on Qubits (E\rhoOQ) framework that enables efficient fault-tolerant preparation of fermionic quantum states. The original method circumvents state preparation by stochastic sampling, but faces a sign problem in fermionic systems leading to a large number of circuits necessary. We resolve this by combining classical stochastic sampling with a linear combination of unitaries method that avoids the exponential circuit scaling that plagued naïve implementations. The resulting algorithm requires \mathcal{O}(M^2) R_Z rotations for circuit preparation, where M is the number of retained basis states. We validate the method for ground and excited states in the Thirring model, including by computing two-point correlation functions relevant to scattering. In this model for fixed accuracy \varepsilon, M is found to scale empirically as M \propto \frac{1}{mg}\log(1/g)\log(1/m). Comments: 9 pages, 5 figures Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat) Report number: FERMILAB-PUB-26-0155-T Cite as: arXiv:2603.22422 [quant-ph]   (or arXiv:2603.22422v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22422 Focus to learn more Submission history From: Henry Lamm [view email] [v1] Mon, 23 Mar 2026 18:01:03 UTC (228 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: hep-lat 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?)