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  • Open Access

Large time-step discretization of adiabatic quantum dynamics

Dong An1,2,*, Pedro C. S. Costa3,4, and Dominic W. Berry4

  • *Contact author: dongan@pku.edu.cn
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Phys. Rev. Research 8, 043098 – Published 28 October, 2026

DOI: https://doi.org/10.1103/kh4h-m8z9

Abstract

Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra computational overhead or complicated quantum control logic. In this work, we show that the time-step sizes in time discretization can be much larger than expected, and the overall complexity is greatly reduced. Remarkably, regardless of the general convergence order of the numerical method, we can choose a uniform time-step size independent of tolerated error and evolution time for sufficiently accurate simulation. Furthermore, with the boundary cancellation condition where the continuous diabatic errors are exponentially suppressed, we provide strong evidence for a superpolynomial convergence of first-order Trotter with uniform time-step size. We apply our analysis to the example of adiabatic unstructured search and show several preferable features of the Trotterized adiabatic approach: It can match the Grover lower bound, it does not require a priori knowledge of the number of marked states, and its performance can be asymptotically comparable with that of the quantum approximate optimization algorithm.

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Phys. Rev. Research 8, 043098– Published 28 October, 2026
  • Received 14 November 2025
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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