Diabatic Quantum Annealing Enables Faster Training of Energy-Based Generative Models with Reduced Validation Error

Training complex generative models, such as restricted Boltzmann machines, often stalls due to the limitations of conventional sampling techniques, which struggle with speed and accuracy. Gilhan Kim, Ju-Yeon Ghym, and Daniel K. Park, from Yonsei University and Seoul National University, present a novel approach using diabatic quantum annealing to generate the unbiased samples crucial for effective model training. Their method overcomes the slow convergence and correlated outputs of classical techniques, achieving faster training and improved performance. By directly mapping the model’s structure onto the quantum hardware, the researchers not only simplify the computational demands but also pave the way for training larger, more complex Boltzmann machines currently beyond the reach of classical methods, offering a significant step forward in the field of machine learning.

This approach aims to accelerate training convergence and improve the quality of generated samples, even with high-dimensional data and intricate dependencies, by harnessing quantum mechanics to navigate complex energy landscapes and identify optimal model parameters. This investigation demonstrates the feasibility and potential benefits of using quantum annealing for training generative models, paving the way for more efficient techniques.

Training seed generative models, such as restricted Boltzmann machines, typically requires unbiased Boltzmann samples, which are difficult to obtain using classical methods. This research addresses this bottleneck by applying a relationship between annealing schedules and effective inverse temperature in diabatic quantum annealing, enabling faster RBM training with lower validation error than classical sampling. The study also identified a systematic temperature misalignment intrinsic to the process, a key finding for optimising future implementations, demonstrating a pathway to leverage quantum annealing for machine learning tasks requiring high-quality sampling.

Quantum Annealing Trains Restricted Boltzmann Machines

This research details the use of quantum annealing, specifically with D-Wave systems, for machine learning tasks, focusing on training restricted Boltzmann machines. It explores the challenges of using quantum hardware for this purpose, including the need for error mitigation and understanding the limitations of current quantum devices, and delves into the theoretical foundations of using quantum annealing for sampling and optimization problems relevant to machine learning.

Restricted Boltzmann machines serve as a key target for this research, as they are a type of generative neural network used for dimensionality reduction, feature learning, and generative modelling. Quantum annealing could offer speedups for training RBMs compared to classical methods, particularly with large datasets or complex models, by efficiently exploring the energy landscape of the RBM. However, current quantum annealers have limitations, including limited qubit connectivity requiring problem embedding, susceptibility to noise and errors, and the need for accurate hardware calibration.

The research emphasizes the connection between quantum annealing and Boltzmann sampling, a method for generating samples from a probability distribution. Quantum annealing can be viewed as a way to approximate Boltzmann sampling, and the concept of effective temperature in quantum annealers is crucial for characterising the shape of the energy landscape explored by the quantum process. Understanding the quantum critical dynamics of the annealing process, and how the system evolves towards the optimal solution, is also important.

Researchers conducted experiments to benchmark the performance of quantum annealing for training RBMs and developed error mitigation techniques to improve accuracy. The performance of the quantum annealer was evaluated on various datasets and compared to classical methods, utilizing D-Wave quantum annealers and the Qiskit open-source framework, considering the connectivity of the D-Wave Pegasus architecture.

Future research directions include improving the scalability of quantum annealing for machine learning, developing fault-tolerant quantum computers, and exploring hybrid algorithms that combine the strengths of both quantum and classical computing. This research highlights the potential of using quantum annealing for practical applications before fully fault-tolerant computers are available, presenting a comprehensive investigation into the potential of quantum annealing for machine learning, acknowledging both the opportunities and the challenges.

Quantum Boltzmann Machines Trained with Annealing Schedules

This research demonstrates the successful application of a relationship between annealing schedules and effective temperature in adiabatic quantum annealing to train restricted Boltzmann machines. By employing schedule-controlled sampling on a quantum annealer, the team generated Boltzmann distributions at specific temperatures and showed that this quantum-assisted approach outperforms classical Markov chain Monte Carlo sampling in both convergence speed and model accuracy. Furthermore, the study identified and corrected for a temperature misalignment inherent in analog quantum computers, improving the reliability of the learning process.

The work establishes a new benchmark in quantum machine learning by training Boltzmann machines directly on full-resolution images, using 1984 qubits, without dimensionality reduction. This method bypasses limitations of classical approaches by allowing training of fully connected Boltzmann machines, which were previously impractical due to sampling difficulties. While current experiments are limited by the sparse connectivity of existing quantum hardware, the principles developed here are applicable to other quantum annealing platforms and could extend to more complex generative models, such as variational autoencoders, as hardware improves. The team also confirmed the correspondence between the quantum process and gate-based quantum circuits through simulations, suggesting broader implementation potential.