Quantum Sampling Algorithms for Near-Term Devices

TL;DR

This paper introduces quantum algorithms for sampling from Gibbs distributions, demonstrating potential speedups over classical methods and applicability to near-term quantum devices like Rydberg atom arrays.

Contribution

It presents a family of quantum algorithms that produce unbiased samples from Gibbs distributions, connecting quantum speedup to phase transitions and enabling implementation on near-term devices.

Findings

Quantum algorithms outperform classical Markov chain methods in specific models.

The approach provides a physical interpretation of quantum speedup related to phase transitions.

Sampling from independent sets can be implemented using Rydberg atom arrays.

Abstract

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.