Original title: Unbiased sampling from Boltzmann distributions with noisy energies
Iwo Sanderski, Gian Gentinetta, Giuseppe Carleo · September 2026
In computational physics, scientists often need to sample states from a thermal spread called the Boltzmann distributionA probability distribution that describes how likely different states of a system are, based on their energy.. When energy estimates have random noise—which happens with machine-learned molecular potentials, variational Monte CarloA method that uses random sampling to approximate the behavior of quantum systems., or quantum computers—that noise skews the sampled results. Older fix methods need the exact variance of the noise and break down if the noise gets too large. To fix this, researchers created the Poisson product estimator. It gives an unbiased, non-negative estimate of the Boltzmann weight. It only requires an upper bound on the energy estimator and stays efficient even under high noise. When testing it on a variational quantum circuitA quantum circuit with adjustable parameters, used to approximate quantum states. without using gradients, they recovered the ground-state energyThe lowest possible energy of a quantum system. for $H_3^+$ in a minimal basis and mapped the energy landscape.
Imagine you're trying to pick the best route for a hike, but your map's distances are blurry. Normally, you'd compare routes by their lengths, but the blur makes it hard. A friend suggests a trick: instead of measuring each route's length, you just need to know the maximum possible length of any route. Then you can still pick the best one, even if the blur is heavy. In this paper, the energy estimates are like the blurry distances, and the Poisson product estimator uses an upper bound to correct the sampling, so you get the right answer despite the noise.
Scientists often simulate molecules or quantum systems where energy calculations are noisy. This noise biases results, making predictions unreliable. The new method removes that bias without needing to know the noise level, so simulations become accurate even when noise is high, which could improve drug design, materials science, and quantum computing.
The abstract does not specify the computational cost of the estimator or its performance on larger systems. It also does not address how to obtain a tight upper bound on the energy estimator in practice, which may be challenging for complex systems.
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Unbiased sampling from Boltzmann distributions with noisy energies — Iwo Sanderski, Gian Gentinetta, Giuseppe Carleo
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.