Periodic Symmetry-Adapted Encoding: Qubit Reduction in Crystalline Electronic Structure

Quantum Physics [Submitted on 4 Jun 2026] Periodic Symmetry-Adapted Encoding: Qubit Reduction in Crystalline Electronic Structure Dario Picozzi We extend the symmetry-adapted encoding (SAE) framework to periodic electronic structure, enabling qubit-efficient quantum simulation of crystalline materials. By constructing a \Gamma-point supercell Hamiltonian from a folded k-point calculation and systematically identifying all applicable space-group symmetry generators -- including spin-parity, point-group, and crystal translation symmetries -- we obtain qubit Hamiltonians with fewer qubits than the Jordan--Wigner starting point. We benchmark diamond, silicon, 3C-SiC, MgO, NaCl, CsCl, h-BN, wurtzite AlN, \alpha-quartz SiO_2, and MgF_2 using active spaces chosen to preserve complete near-degenerate frontier manifolds across cubic, hexagonal, trigonal, and tetragonal space groups. Across the suite the periodic SAE removes 4--8 qubits. The B2 CsCl benchmark realises eight independent Boolean generators, i.e. a symmetry group isomorphic to \mathbb{Z}_2^8, reducing CAS(6,7) from 14 to 6 qubits. This exceeds the \mathbb{Z}_2^5 maximum of molecular SAE, where only two spin parities and at most three independent Boolean point-group generators are available, because the folded crystal supplies three additional half-translation symmetries. Noiseless UCCSD-VQE benchmarks against exact diagonalisation in the active-space sector show that the reduced encodings preserve the target energies to well below chemical accuracy while reducing variational parameter counts by 3--8\times and CNOT counts by up to 309\times. The largest circuit savings occur when translation and point-group generators act independently in the active space, demonstrating that periodic symmetry can be converted directly into both qubit and ansatz compression. The method is implemented in the open-source QuantumSymmetry package and requires no manual specification of symmetry generators. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05777 [quant-ph]   (or arXiv:2606.05777v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05777 Focus to learn more Submission history From: Dario Picozzi [view email] [v1] Thu, 4 Jun 2026 07:05:29 UTC (11,924 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 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?)