Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry

• URL: http://arxiv.org/abs/2605.16016v1
• Date: Fri, 15 May 2026 14:50:29 GMT
• Title: Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry
• Abstract summary: We introduce a new decomposition principle that goes beyond commutativity, grouping Hamiltonian terms into local three-site clusters.<n>We show that three-site generators fall into at most four SU(2)-symmetry classes, each admitting an effective two-qubit SU(4) representation.<n>We demonstrate the proposed method on several physically relevant spin-lattice models, where the reduced cluster structure can even realise the second-order product formula.
• Score: 3.7159810638207813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions typically rely on direct commutativity among Hamiltonian terms in a chosen operator representation, which can lead to large residual errors and deep circuits for complex, practically relevant many-body quantum systems. We address this fundamental bottleneck by introducing a new decomposition principle that goes beyond commutativity, grouping Hamiltonian terms into local three-site clusters according to the underlying SU(2) symmetry of the local dynamics. We show that three-site generators fall into at most four SU(2)-symmetry classes, each admitting an effective two-qubit SU(4) representation with exact and efficient implementations. By reducing the number of clusters, this decomposition principle substantially suppresses commutator-induced errors and circuit overhead while preserving underlying physical structures that commutativity-based decompositions may violate. We demonstrate the proposed method on several physically relevant spin-lattice models, where the reduced cluster structure can even realise the second-order product formula without doubling the circuit depth, as would be required by conventional decompositions. Numerical simulations of a Kagome Heisenberg model with triangular spin-chirality interactions show that the proposed method reduces both state infidelity and average spin-chirality bias by more than three orders of magnitude compared with conventional decompositions, while using substantially fewer gates. These results establish local symmetry as a flexible and practical design principle for product-formula simulation, opening a route to more accurate and hardware-efficient simulations of broader classes of many-body systems.

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