Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace

• URL: http://arxiv.org/abs/2601.01550v1
• Date: Sun, 04 Jan 2026 14:50:15 GMT
• Title: Time-Dependent Hamiltonian Simulation in the Low-Energy Subspace
• Authors: Shuo Zhou, Zhaokai Pan, Weiyuan Gong, Tongyang Li,
• Abstract summary: Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics.<n>We show how much we can improve upon the standard performance guarantee assuming the initial state is supported on a low-energy subspace.
• Score: 16.596052084718124
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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