Partition Function Estimation Using Analog Quantum Processors

TL;DR

This paper explores using programmable superconducting flux qubit D-Wave quantum annealers to estimate the partition function of Ising models, demonstrating comparable accuracy to classical methods and highlighting the efficiency of certain annealing protocols.

Contribution

It introduces a novel quantum annealing-based method for partition function estimation, leveraging energy spectrum sampling to enable thermodynamic calculations at arbitrary temperatures.

Findings

Quantum annealers can produce accurate partition function estimates.

Fast quench-like anneals yield high-quality ensemble distributions.

Achieved a logarithmic relative error of 7.6e-6 with minimal QPU time.

Abstract

We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like reverse quantum anneals, and standard linear-ramp quantum annealing. The control parameters used to attenuate the quality of the simulations are the effective analog energy scale of the J coupling, the total annealing time, and for the case of reverse annealing the anneal-pause. The core estimation technique is to sample across the energy spectrum of the classical Hamiltonian of interest, and therefore obtain a density of states estimate for each energy level, which in turn can be used to compute an estimate of the partition function with some sampling error. This estimation technique is powerful because once the distribution is sampled it allows thermodynamic quantity computation at arbitrary temperatures. On a $25$ spin $\pm J$ hardware graph native Ising model we find parameter regimes of the D-Wave processors that provide comparable result quality to two standard classical Monte Carlo methods, Multiple Histogram Reweighting and Wang-Landau. Remarkably, we find that fast quench-like anneals can quickly generate ensemble distributions that are very good estimates of the true partition function of the classical Ising model; on a Pegasus graph-structured QPU we report a logarithmic relative error of $7.6 \times 10^{-6}$, from $171,000$ samples generated using $0.2$ seconds of QPU time with an anneal time of $8$ nanoseconds per sample which is interestingly within the closed system dynamics timescale of the superconducting qubits.