Performance Evaluation of Adiabatic Quantum Computation via Quantum Speed Limits and Possible Applications to Many-Body Systems

TL;DR

This paper investigates the fundamental limits of adiabatic quantum computation using quantum speed limits, analyzing how these bounds relate to system performance, phase transitions, and thermodynamic limits.

Contribution

It introduces a fidelity bound based on quantum speed limits for adiabatic states, applicable to many-body systems and phase transition analysis.

Findings

Derived a tight fidelity bound for adiabatic evolution

Analyzed the impact of phase transitions on quantum speed limits

Extended bounds to thermodynamic limit scenarios

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.