Fault-tolerant quantum simulation of the Pauli-Breit Hamiltonian for ab initio hybrid quantum-classical molecular design with applications to photodynamic therapy
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Quantum Physics arXiv:2601.18898 (quant-ph) [Submitted on 26 Jan 2026] Title:Fault-tolerant quantum simulation of the Pauli-Breit Hamiltonian for ab initio hybrid quantum-classical molecular design with applications to photodynamic therapy Authors:Emil Zak View a PDF of the paper titled Fault-tolerant quantum simulation of the Pauli-Breit Hamiltonian for ab initio hybrid quantum-classical molecular design with applications to photodynamic therapy, by Emil Zak View PDF Abstract:Relativistic spin effects drive subtle molecular phenomena ranging from intersystem crossing in photodynamic therapy to spin-mediated catalysis and high-resolution spectroscopy. These effects are described by the Pauli-Breit Hamiltonian, which extends the nonrelativistic electronic Hamiltonian by including one- and two-electron spin-orbit and spin-spin interactions. First-principles simulations of the full Pauli-Breit Hamiltonian rapidly become intractable on classical computers due to the exponential growth of the Hilbert space and the complexity of two-body spin-dependent terms. We propose a fault-tolerant quantum algorithm for computing molecular energy levels and properties governed by the Pauli-Breit Hamiltonian. Our approach block-encodes the relativistic Hamiltonian in a second-quantized, doubly factorized representation. By reformulating the Hamiltonian in a symmetry-adapted Majorana basis, we construct efficient linear-combination-of-unitaries circuits that encode spin-orbit interactions without effective or mean-field approximations. We introduce spin-controlled Pauli-SWAP networks that decouple spin and orbital control logic, enabling a unified treatment of relativistic spin mixing with only modest overhead relative to spin-free simulations. We analyze quantum resources in terms of logical qubits and T-gate complexity, showing that explicit spin degrees of freedom do not worsen the asymptotic scaling. The prefactor is reduced by a factor of two compared to direct linear-combination-of-unitaries approaches. Finally, we outline a hybrid quantum-classical workflow for designing photodynamic therapy photosensitizers, artificial photosynthesis catalysts, and other systems where accurate relativistic spin effects are essential. Comments: Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph) Cite as: arXiv:2601.18898 [quant-ph] (or arXiv:2601.18898v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18898 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Emil Zak [view email] [v1] Mon, 26 Jan 2026 19:11:01 UTC (1,812 KB) Full-text links: Access Paper: View a PDF of the paper titled Fault-tolerant quantum simulation of the Pauli-Breit Hamiltonian for ab initio hybrid quantum-classical molecular design with applications to photodynamic therapy, by Emil ZakView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: physics physics.chem-ph 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)