Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1907.03769 · Annals of Physics

Error-run-time trade-off in the adiabatic approximation beyond scaling relations

M.R. Passos, M.M. Taddei, R.L. de Matos Filho

Published Apr 17, 2020• 3 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2020.168172

Related papers

Accuracy versus run time in an adiabatic quantum search

A. T. Rezakhani, Artem Pimachev, Daniel A. Lidar

Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.

arXiv:1008.0863•Physical Review A•Nov 9, 2010•69 citations

Computable upper bounds for the adiabatic approximation errors

Baomin Yu, HuaiXin Cao, Zhihua Guo +1 more

Science China Physics Mechanics and Astronomy•Aug 4, 2014•11 citations

A note on the switching adiabatic theorem

Alexander Elgart, George A. Hagedorn

We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class Gα as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g−2 |ln g |6α. Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.

arXiv:1204.2318•Journal of Mathematical Physics•Sep 18, 2012•45 citations

Quantitative sufficient conditions for adiabatic approximation

HuaiXin Cao, Zhihua Guo, ZhengLi Chen +1 more

Science China Physics Mechanics and Astronomy•May 23, 2013•24 citations

A Note on the Switching Adiabatic Theorem

Alexander Elgart, George A. Hagedorn

We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class Gα as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g−2 | ln g | α. Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.

•Jan 1, 2012•48 citations

Extending the Adiabatic Theorem

Rachel Berkowitz

Physics•Apr 1, 2026•0 citations
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.