Continuous-time quantum optimisation without the adiabatic principle

TL;DR

This paper proposes a new physical motivation for continuous-time quantum optimization algorithms based on Planck's principle, leading to monotonic schedules that differ from traditional adiabatic approaches and revealing limitations of reverse annealing.

Contribution

It introduces Planck's principle as the foundation for continuous-time quantum algorithms, moving beyond the adiabatic principle and providing new insights into quantum annealing schedules.

Findings

Monotonic schedules justified by Planck's principle.

Limitations of reverse quantum annealing in isolated systems.

New physical motivation for non-adiabatic quantum algorithms.

Abstract

Continuous-time quantum algorithms for combinatorial optimisation problems, such as quantum annealing, have previously been motivated by the adiabatic principle. A number of continuous-time approaches exploit dynamics, however, and therefore are no longer physically motivated by the adiabatic principle. In this work, we take Planck's principle as the underlying physical motivation for continuous-time quantum algorithms. Planck's principle states that the energy of an isolated system cannot decrease as the result of a cyclic process. We use this principle to justify monotonic schedules in quantum annealing, which are not adiabatic. This approach also highlights the limitations of reverse quantum annealing in an isolated system.