The relationship between minimum gap and success probability in adiabatic quantum computing

TL;DR

This paper investigates how the success probability in adiabatic quantum computing relates to the minimum energy gap, revealing a complex structure that can be approximated by specific parameters in small and larger systems.

Contribution

It demonstrates that success probability can be modeled as a function of minimum gap, evolution stage, and time, highlighting a structured relationship in adiabatic algorithms.

Findings

Success probability correlates with minimum gap and evolution stage.

The structured relationship persists in larger quantum systems.

A generic adiabatic algorithm exhibits rich distribution patterns.

Abstract

We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap $\Delta_{min}$ between the ground and first excited states, investigating to what extent the success probability for an ensemble of problem Hamiltonians can be fitted by a function of $\Delta_{min}$ and the computation time $T$. We study a generic adiabatic algorithm and show that a rich structure exists in the distribution of $P$ and $\Delta_{min}$. In the case of two qubits, $P$ is to a good approximation a function of $\Delta_{min}$, of the stage in the evolution at which the minimum occurs and of $T$. This structure persists in examples of larger systems.