Abstract
The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound is characterized by the counterdiabatic Hamiltonian and can be used to evaluate the worst case performance of the adiabatic quantum computation. The result is improved by imposing additional conditions and we examine several models to find a tight bound. We also derive a different type of quantum speed limits that is meaningful even when we take the thermodynamic limit. By using solvable spin models, we study how the performance and the bound are affected by phase transitions.
Highlights
Knowing the fundamental speed limit for a dynamical process is an important problem in physics and is relevant to a broad range of research fields
Among many possible applications [6,7,8,9,10,11,12,13,14], we focus our attention on adiabatic quantum computation (AQC)
We have discussed the quantum speed limits (QSLs) applied to the AQC
Summary
Keisuke Suzuki Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan. Kazutaka Takahashi Institute of Innovative Research, Tokyo Institute of Technology, Kanagawa 226-8503, Japan (Received 7 January 2020; revised 12 April 2020; accepted 24 June 2020; published 15 July 2020). The quantum speed limit specifies a universal bound of the fidelity between the initial state and the timeevolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the timeevolved state. The bound is characterized by the counterdiabatic Hamiltonian and can be used to evaluate the worst case performance of the adiabatic quantum computation. By using solvable spin models, we study how the performance and the bound are affected by phase transitions
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