Fault tolerant computation of the static structure factor and finite size effects
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Quantum Physics arXiv:2606.27734 (quant-ph) [Submitted on 26 Jun 2026] Title:Fault tolerant computation of the static structure factor and finite size effects Authors:Rishabh Bhardwaj, Alexander Reed Muñoz, Travis E. Jones, John Golden View a PDF of the paper titled Fault tolerant computation of the static structure factor and finite size effects, by Rishabh Bhardwaj and 2 other authors View PDF Abstract:Fault-tolerant quantum algorithms offer a promising pathway for estimating the ground-state energies of periodic materials that are beyond the practical reach of classical electronic-structure methods. A remaining challenge is finite-size mitigation: quantum algorithms evaluate a finite supercell or finite Brillouin-zone mesh, while materials properties are defined in the thermodynamic limit. In this work we develop a quantum post-processing strategy for the leading two-body finite-size correction. After one-body shell effects are reduced by twist averaging, the dominant residual error is controlled by long-wavelength density fluctuations, which are encoded in the small-momentum static structure factor $S(q)$. We formulate the corresponding operator in a Bloch-orbital basis, construct its block encoding through the density operator, and estimate its ground-state expectation value using an amplified Hadamard test. We also introduce adaptive global and local binary search procedures for identifying the infrared fitting window used to reconstruct the two-body finite size error correction. The resulting cost remains subleading relative to the main ground-state energy estimation routine: the structure-factor correction has leading $\tilde{O}(N_bN_k)^3$ dependence on the Bloch-orbital basis size, avoids the large plane-wave prefactor of full Hamiltonian simulation, and requires only $\tilde{O}(N_bN_k)$ logical qubits. This provides a fault-tolerant alternative to down-sampling, replacing repeated energy calculations on larger cells with targeted measurements of the infrared density correlations that control the finite-size effects. Comments: Subjects: Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2606.27734 [quant-ph] (or arXiv:2606.27734v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.27734 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rishabh Bhardwaj [view email] [v1] Fri, 26 Jun 2026 05:31:08 UTC (1,505 KB) Full-text links: Access Paper: View a PDF of the paper titled Fault tolerant computation of the static structure factor and finite size effects, by Rishabh Bhardwaj and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.mtrl-sci cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)