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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.16016 |
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| _version_ | 1866916016179642368 |
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| author | Negishi, Naoki Yang, Bo |
| author_facet | Negishi, Naoki Yang, Bo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry Negishi, Naoki Yang, Bo Quantum Physics Strongly Correlated Electrons 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. |
| title | Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.16016 |