Using domain walls to benchmark fast quantum anneals

We consider the distribution of domain walls arising in ground states of frustrated 1-dimensional Ising spin chains with anti-parallel boundary spins. For ideal chains, a sine-squared particle-in-a-box distribution of domain walls is expected in the quantum setting, and a uniform distribution expected classically. However, for chains with random imperfections, prior work [Chancellor et al., npj Quantum Inf. 8, 73, 2022] found that the distribution in a physical implementation corresponded to neither. Instead, the domain wall distribution forms a U-shaped profile arising from a classical model with random fields, where the combination of averaging over these fields and thermal averaging produces the characteristic U-shape. With D-Wave's newer fast anneal feature, we access anneal times shorter than the coherence time and observe the expected coherent quantum behavior in the form of a sine-squared distribution. For the shortest available anneal time, the dynamics have not yet reached the sine-squared shape and instead display a different U-shape in the middle of the chains. This motivates using the extent of the domain wall distribution tail in this regime as a platform independent metric that provides a signature of both coherence time and noise levels.