Abstract:Hamiltonian simulations are key subroutines in adiabatic quantum computation and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. Previous studies have shown that the low-energy assumption can reduce the resource requirements of standard time-independent Hamiltonian simulation algorithms. However, whether such advantages extend to time-dependent Hamiltonian simulation remains open. In this paper, we consider the adiabatic regime where the relevant low-energy subspace is spanned by a fixed number of low-energy eigenstates and separated from the rest of the spectrum by a gap. We show that, for simulating spin Hamiltonians by product formulas, the explicit system size dependence in the leading commutator-scaling term can be replaced by a low-energy scale up to logarithmic factors. 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 conduct numerical experiments on adiabatic state preparation of an illustrative example system to support our theoretical findings. Finally, we prove a lower bound of query complexity for generic time-dependent Hamiltonian simulations.
From: Shuo Zhou [view email]
[v1]
Sun, 4 Jan 2026 14:50:15 UTC (276 KB)
[v2]
Wed, 5 Aug 2026 13:29:42 UTC (997 KB)
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