Boltzmann sampling by diabatic quantum annealing

Elizabeth Crosson, Daniel A. Lidar

Richard Li, Daniel A. Lidar

Ju-Yeon Gyhm, Kim, Gilhan, Hyukjoon Kwon +1 more

Boltzmann sampling is a central component of many computational frameworks, including numerous algorithms in machine learning. Although quantum annealers have been investigated as potential fast Boltzmann samplers, their dependence on environmental noise makes precise control of the effective temperature difficult, introducing uncertainty into the sampling process. As an alternative, we propose diabatic quantum annealing-a faster, purely unitary process-as a controllable Boltzmann sampler in which the effective temperature is determined by the annealing rate. Using the ferromagnetic Ising model and the Sherrington-Kirkpatrick model as test cases, we demonstrate that this method achieves rapid and accurate sampling in the high-temperature regime.

Gilhan Kim, Daniel K. Park

Energy-based models provide a natural bridge between statistical physics and machine learning by representing data through structured energy landscapes. Boltzmann machines are a particularly compelling class of such models for capturing complex interactions among latent variables, but their use in modern generative learning has been limited by the classical intractability of sampling from general (non-restricted) Boltzmann distributions. Here we develop a quantum-annealing-based framework that enables variational autoencoders with general Boltzmann priors. The framework employs three complementary annealing modes tailored to different stages of learning and deployment: diabatic quantum annealing provides unbiased Boltzmann samples for efficient training, slower annealing concentrates samples near low-energy configurations of the learned prior for unconditional generation, and conditional annealing with external fields steers the learned energy landscape toward attribute-specific regions for conditional generation and semantic editing. Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable training and high-quality generation on MNIST, Fashion-MNIST, and CelebA, achieving faster convergence and lower reconstruction loss than a Gaussian-prior VAE with the same encoder-decoder architecture. Beyond generation, the learned energy function provides out-of-distribution detection signals that add discriminative power beyond reconstruction loss. We demonstrate that these scores separate in-distribution samples from held-out digit classes in one-class MNIST experiments and improve the detection of market regime shifts in financial data. These results establish quantum annealing as a practical and controllable physical mechanism for energy-based representation learning and generative modeling beyond the reach of tractable classical approaches.

Gilhan Kim, Ju-Yeon Gyhm, Daniel K. Park

Energy-based generative models, such as restricted Boltzmann machines (RBMs), require unbiased Boltzmann samples for effective training. Classical Markov chain Monte Carlo methods, however, converge slowly and yield correlated samples, making large-scale training difficult. We address this bottleneck by applying the analytic relation between annealing schedules and effective inverse temperature in diabatic quantum annealing. By implementing this prescription on a quantum annealer, we obtain temperature-controlled Boltzmann samples that enable RBM training with faster convergence and lower validation error than classical sampling. We further identify a systematic temperature misalignment intrinsic to analog quantum computers and propose an analytical rescaling method that mitigates this hardware noise, thereby enhancing the practicality of quantum annealers as Boltzmann samplers. In our method, the model's connectivity is set directly by the qubit connectivity, transforming the computational complexity inherent in classical sampling into a requirement on quantum hardware. This shift allows the approach to extend naturally from RBMs to fully connected Boltzmann machines, opening opportunities inaccessible to classical training methods.

Hiroki Ikoma