Non-classical Role of Potential Energy in Adiabatic Quantum Annealing

TL;DR

This paper explores how potential energy influences adiabatic quantum annealing, revealing that quantum particles can locate deeper minima faster, contrasting with classical search limitations, and discusses the impact of quantum phase transitions.

Contribution

It uncovers a non-classical role of potential energy in quantum annealing, especially how it affects the search efficiency for potential minima.

Findings

Quantum particles locate deeper minima faster.

Classical particles do not exploit potential depth.

Quantum phase transitions influence adiabatic dynamics.

Abstract

Adiabatic quantum annealing is a paradigm of analog quantum computation, where a given computational job is converted to the task of finding the global minimum of some classical potential energy function and the search for the global potential minimum is performed by employing external kinetic quantum fluctuations and subsequent slow reduction (annealing) of them. In this method, the entire potential energy landscape (PEL) may be accessed simultaneously through a delocalized wave-function, in contrast to a classical search, where the searcher has to visit different points in the landscape (i.e., individual classical configurations) sequentially. Thus in such searches, the role of the potential energy might be significantly different in the two cases. Here we discuss this in the context of searching of a single isolated hole (potential minimum) in a golf-course type gradient free PEL. We show, that the quantum particle would be able to locate the hole faster if the hole is deeper, while the classical particle of course would have no scope to exploit the depth of the hole. We also discuss the effect of the underlying quantum phase transition on the adiabatic dynamics.