Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918271625723904 |
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| author | Zhou, Shuo Pan, Zhaokai Gong, Weiyuan Li, Tongyang |
| author_facet | Zhou, Shuo Pan, Zhaokai Gong, Weiyuan Li, Tongyang |
| contents | Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian simulations, a comprehensive understanding of quantum simulation algorithms for time-dependent Hamiltonians under the low-energy assumption remains limited hitherto. In this paper, we investigate how much we can improve upon the standard performance guarantee assuming the initial state is supported on a low-energy subspace. In particular, we compute the Trotter number of digital quantum simulation based on product formulas for time-dependent spin Hamiltonians under the low-energy assumption that the initial state is supported on a small number of low-energy eigenstates, and show improvements over the standard cost for simulating full unitary simulations. Technically, we derive the low-energy simulation error with commutator scaling for product formulas by leveraging adiabatic perturbation theory to analyze the time-variant energy spectrum of the underlying Hamiltonian. We further discuss the applications to simulations of non-equilibrium quantum many-body dynamics and adiabatic state preparation. Finally, we prove a lower bound of query complexity for generic time-dependent Hamiltonian simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace Zhou, Shuo Pan, Zhaokai Gong, Weiyuan Li, Tongyang Quantum Physics Data Structures and Algorithms Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian simulations, a comprehensive understanding of quantum simulation algorithms for time-dependent Hamiltonians under the low-energy assumption remains limited hitherto. In this paper, we investigate how much we can improve upon the standard performance guarantee assuming the initial state is supported on a low-energy subspace. In particular, we compute the Trotter number of digital quantum simulation based on product formulas for time-dependent spin Hamiltonians under the low-energy assumption that the initial state is supported on a small number of low-energy eigenstates, and show improvements over the standard cost for simulating full unitary simulations. Technically, we derive the low-energy simulation error with commutator scaling for product formulas by leveraging adiabatic perturbation theory to analyze the time-variant energy spectrum of the underlying Hamiltonian. We further discuss the applications to simulations of non-equilibrium quantum many-body dynamics and adiabatic state preparation. Finally, we prove a lower bound of query complexity for generic time-dependent Hamiltonian simulations. |
| title | Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.01550 |