Residual Energies after Slow Quantum Annealing

TL;DR

This paper investigates how residual energy decreases as the inverse square of annealing time in slow quantum annealing, supported by numerical simulations and theoretical derivation based on the adiabatic theorem.

Contribution

It demonstrates the inverse square law for residual energy decay in quantum annealing and provides a theoretical explanation for this behavior.

Findings

Residual energy decreases as the inverse square of annealing time.

Numerical calculations confirm the theoretical prediction.

The behavior is explained through the quantum adiabatic theorem.

Abstract

Features of the residual energy after the quantum annealing are investigated. The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.