Unbiased KL-divergence estimator for high-entropy quantum-simulation distributions

Develop an unbiased estimator for the Kullback–Leibler divergence, in either direction KL[p, p~] or KL[p~, p], that remains accurate and informative for large-scale, high-entropy probability distributions produced by computational-basis measurements of quenches in the transverse-field Ising model, so divergence between quantum annealer output distributions and ground-truth distributions can be quantified without requiring exponentially many samples.

Background

To assess the closeness between distributions obtained from the quantum annealer and classical ground-truth simulations, the authors examined various divergence measures (cross entropy, KL divergences, classical fidelity). Because the entropy of the distributions grows with the number of spins, sampling-based estimates become impractical at larger sizes.

The authors ultimately relied on a correlation-based metric because they could not identify an unbiased, practically informative estimator for KL divergence suitable for the high-entropy regime relevant to their experiments. A robust estimator would enable principled benchmarking without incurring exponentially growing sample complexity.