Scaling and diabatic effects in quantum annealing with a D-Wave device

TL;DR

This paper investigates the effects of scaling and diabatic processes in quantum annealing on a D-Wave device, revealing an optimal annealing rate that balances quantum fluctuations and noise impacts, with implications for larger systems.

Contribution

It introduces a phenomenological model capturing the interplay of quantum fluctuations and noise in quantum annealing, validated by experiments and numerical simulations.

Findings

Optimal annealing rate depends on system size and minimizes residual energy and magnetization deviation.

The model incorporates Kibble-Zurek mechanism and noise effects to explain scaling behavior.

Optimal annealing time exceeds individual qubit coherence times, impacting quantum annealing strategies.

Abstract

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on $L \times L$ lattices with $L \le 32$. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal $L$ dependent annealing rate $v$ for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of $v$ and $L$-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when $v$ is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.