Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification

Quantum Physics arXiv:2608.11579 (quant-ph) [Submitted on 12 Aug 2026] Title:Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification Authors:Zhaohui Yang, Yuwei Han, Ruiyun Zhang, Dawei Ding, Jianxin Chen, Yuan Feng, Yuan Xie View a PDF of the paper titled Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification, by Zhaohui Yang and 6 other authors View PDF HTML (experimental) Abstract:Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, adaptively reducing active Pauli rows and emitting eligible two-qubit blocks other than single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It strictly Pareto-dominates prior state-of-the-art compilers, requiring 1.14--1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67$\times$ on average. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.11579 [quant-ph] (or arXiv:2608.11579v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.11579 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhaohui Yang [view email] [v1] Wed, 12 Aug 2026 02:38:42 UTC (628 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification, by Zhaohui Yang and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)