Fault-tolerant simulation of the electronic structure using Projector Augmented-Waves and Bloch orbitals

Quantum Physics [Submitted on 13 Apr 2026] Fault-tolerant simulation of the electronic structure using Projector Augmented-Waves and Bloch orbitals Rishabh Bhardwaj, Alexander Reed Muñoz, Travis E. Jones, John Golden Strongly correlated materials are a natural target for fault-tolerant quantum computers, but they require tools beyond those developed for molecules. Electronic wavefunctions vary rapidly near nuclei yet remain delocalized across many unit cells, and bulk properties must be converged systematically with respect to finite-size errors. To resolve such issues, we present the Bloch--UPAW framework that combines Bloch-orbital k-space structure with unitary projector-augmented-wave (UPAW) augmentation. The UPAW Hamiltonian, expressed directly in the Bloch basis, retains explicit control of Brillouin-zone sampling, and incorporates near-nuclear physics through strictly local on-site corrections. The construction is independent of the underlying one-particle representation, so it applies to both plane-wave and localized bases, and it handles supercells for symmetry-breaking phenomena more efficiently. We derive a linear-combination-of-unitaries decomposition and a block-encoding circuit suitable for qubitization; UPAW augmentation adds one ancilla qubit and no Toffoli gates at leading order relative to a Bloch-only block encoding. Asymptotically, the Toffoli cost scales as \mathcal{O}(N_k^3) when refining the k-mesh and as \mathcal{O}(N_a^{3.5}) when enlarging the supercell, enabling convergence to be steered by the most favorable route for a given material. Resource estimates for bulk diamond show approximately an order-of-magnitude reduction in Toffoli count relative to prior work on periodic solids. Comments: 11+14 pages, 6 figures Subjects: Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2604.12142 [quant-ph]   (or arXiv:2604.12142v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.12142 Focus to learn more Submission history From: Rishabh Bhardwaj [view email] [v1] Mon, 13 Apr 2026 23:46:58 UTC (790 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.mtrl-sci cond-mat.str-el 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?)