{"ID":2822899,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.01550","arxiv_id":"2601.01550","title":"Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace","abstract":"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.","short_abstract":"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-dep...","url_abs":"https://arxiv.org/abs/2601.01550","url_pdf":"https://arxiv.org/pdf/2601.01550v1","authors":"[\"Shuo Zhou\",\"Zhaokai Pan\",\"Weiyuan Gong\",\"Tongyang Li\"]","published":"2026-01-04T14:50:15Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.DS\"]","methods":"[]","has_code":false}