Large time-step discretization of adiabatic quantum dynamics
4 affiliations
- 1Peking University
- 2University of Maryland, College Park
- 3ContinoQuantum
- 4Macquarie University
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 knowledge of the number of marked states, and its performance can be asymptotically comparable with that of the quantum approximate optimization algorithm.
Versions
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BibTeX
@article{an2026large,
title = {{Large time-step discretization of adiabatic quantum dynamics}},
author = {Dong An and Pedro C. S. Costa and Dominic W. Berry},
journal = {Physical Review Research},
year = {2026},
month = oct,
doi = {10.1103/kh4h-m8z9},
url = {http://link.aps.org/doi/10.1103/kh4h-m8z9},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Large time-step discretization of adiabatic quantum dynamics
AU - Dong An
AU - Pedro C. S. Costa
AU - Dominic W. Berry
PY - 2026
DA - 2026/10/28
JO - Physical Review Research
DO - 10.1103/kh4h-m8z9
UR - http://link.aps.org/doi/10.1103/kh4h-m8z9
AB - 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 knowledge of the number of marked states, and its performance can be asymptotically comparable with that of the quantum approximate optimization algorithm.
SN - 2643-1564
ER -