Symmetry-adapted qubit encoding with complete active space and Bravyi--Kitaev mapping for quantum chemistry on a quantum computer

Quantum Physics [Submitted on 4 Jun 2026] Symmetry-adapted qubit encoding with complete active space and Bravyi--Kitaev mapping for quantum chemistry on a quantum computer Dario Picozzi, Jonathan Tennyson We present a symmetry-adapted qubit encoding with complete active space (SAE-CAS) for quantum chemistry on fault-tolerant and near-term quantum processors. Building on exact-symmetry encodings, we extend symmetry-adapted mappings to approximate Z-symmetries corresponding to frozen-core and virtual orbitals, thereby reducing qubit requirements without significant loss of accuracy. We derive the mapping from the second-quantised Hamiltonian to active-space qubit Hamiltonians, prove its equivalence to the canonical CAS Hamiltonian with frozen-core and virtual-orbital projection, and integrate it with point-group and spin-parity symmetry encodings via affine Clifford transformations to maximise qubit reduction while preserving the target symmetry sector. The same framework also accommodates the Bravyi--Kitaev mapping, yielding an SAE-CAS-BK variant that is unitarily equivalent to SAE-CAS. Numerical benchmarking on nine small molecules using UCCSD and a hardware-efficient shifted-circular-alternating (HE-SCA) ansatz shows that SAE-CAS reduces qubit counts and Pauli-operator weight, yields shallower circuits with fewer parameters, and often accelerates VQE convergence; with HE-SCA it consistently reaches CAS reference energies in cases where JW-CAS does not converge within the tested budgets. We provide an open-source implementation in the Python package QuantumSymmetry. SAE-CAS offers a route to resource-efficient molecular simulations on fault-tolerant and near-term quantum processors. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05865 [quant-ph]   (or arXiv:2606.05865v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05865 Focus to learn more Submission history From: Dario Picozzi [view email] [v1] Thu, 4 Jun 2026 08:43:16 UTC (4,958 KB) Access Paper: 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?)