Optimization versus fair sampling in quantum annealing: An exactly characterized frustrated Ising benchmark
Abstract
Reaching a degenerate ground-state manifold and sampling it uniformly are distinct properties of a quantum annealer. We quantify this distinction using an Ising ring with additional couplings between maximally separated sites. For antiferromagnetic benchmark couplings and N ≥ 5, we derive the exact ground-state energy, degeneracy, and defect structure for each congruence class of N modulo four. This classification separates ground-state hit probability from conditional sampling bias. We embed instances with up to 162 logical spins on a D-Wave Advantage processor using length-two chains and compare its output with simulated annealing on the embedded and logical problems. For a frustrated N=83 instance, the processor visits 164 of the 166 exact ground states, yet the conditional distributions over states and defect sectors remain nonuniform. For N=160, the processor has a larger ground-state hit probability than logical simulated annealing (0.869 versus 0.519), but also a larger total-variation distance from uniformity (0.317 versus 0.136). A pause during the anneal raises the ground-state hit probability from 0.42 to 0.86 without restoring uniform sampling. These results identify a relaxation window and demonstrate that optimization success and sampling quality need not improve together, providing an exactly characterized benchmark for open-system quantum annealing.
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BibTeX
@misc{hitomi2026optimization,
title = {{Optimization versus fair sampling in quantum annealing: An exactly characterized frustrated Ising benchmark}},
author = {Masaru Hitomi and Masayuki Ohzeki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29035},
eprint = {2610.29035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29035},
}
RIS
TY - UNPB
TI - Optimization versus fair sampling in quantum annealing: An exactly characterized frustrated Ising benchmark
AU - Masaru Hitomi
AU - Masayuki Ohzeki
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29035
UR - https://arxiv.org/abs/2610.29035
AB - Reaching a degenerate ground-state manifold and sampling it uniformly are distinct properties of a quantum annealer. We quantify this distinction using an Ising ring with additional couplings between maximally separated sites. For antiferromagnetic benchmark couplings and N ≥ 5, we derive the exact ground-state energy, degeneracy, and defect structure for each congruence class of N modulo four. This classification separates ground-state hit probability from conditional sampling bias. We embed instances with up to 162 logical spins on a D-Wave Advantage processor using length-two chains and compare its output with simulated annealing on the embedded and logical problems. For a frustrated N=83 instance, the processor visits 164 of the 166 exact ground states, yet the conditional distributions over states and defect sectors remain nonuniform. For N=160, the processor has a larger ground-state hit probability than logical simulated annealing (0.869 versus 0.519), but also a larger total-variation distance from uniformity (0.317 versus 0.136). A pause during the anneal raises the ground-state hit probability from 0.42 to 0.86 without restoring uniform sampling. These results identify a relaxation window and demonstrate that optimization success and sampling quality need not improve together, providing an exactly characterized benchmark for open-system quantum annealing.
ER -