Using domain walls to benchmark fast quantum anneals

Abstract

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.

The paper studies whether domain-wall position distributions in frustrated Ising chains can benchmark coherence and noise in fast quantum annealing. Ferromagnetic chains with oppositely pinned ends support a single domain wall: an ideal coherent ground state has a sine-squared position profile, whereas classical thermal sampling is uniform without disorder and becomes U-shaped after averaging over random longitudinal fields. Experiments on D-Wave Advantage 4.1 embed 468 twelve-spin chains and use $10^4$ repetitions at anneal durations of 5, 10, and 30 ns and $20\,\mu$s. After postselecting single-domain-wall outcomes, the 10 ns distribution approximates the sine-squared profile; 5 ns produces an M-shaped profile, while longer anneals produce U-shaped distributions. Single-wall outcomes constitute approximately 70.7%, 91.2%, and 99.6% of samples at 5, 10, and 30 ns, respectively. Closed-system Schrödinger evolution with Gaussian static longitudinal disorder, fitted to the 5 ns data, gives disorder strength $0.101\pm0.007$ GHz. Combining this with thermal-distribution fits gives an estimated temperature of $17.53\pm2.34$ mK. A phenomenological mixture of coherent and thermal distributions fits the 10 ns data with thermal weight $0.105\pm0.025$. The proposed benchmark is the normalized number of positions over which probability rises monotonically from an end toward the chain centre. Simulations explore its dependence on anneal duration and disorder. The study uses short chains; the paper notes that its Monte Carlo fitting would be impractical for larger systems. Cross-platform applicability remains untested, particularly for Rydberg devices, where loss dominates and the metric’s additional information remains to be established.