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IEEE International Conference on Quantum Computing and Engineering (QCE)

Quantum-Assisted Machine Learning Framework: Training and Evaluation of Boltzmann Machines Using Quantum Annealers

Jose P. Pinilla, Steven J. E. Wilton

Published Sep 15, 2024• 1 citation
Publisher

Abstract

This paper describes the components and configurations available in a new quantum-assisted machine learning (QAML) framework. QAML is an open source package that provides a new and flexible test-bed for algorithms to train and evaluate Boltzmann machines (BMs) using quantum annealers. Quantum annealing processors enable the training capabilities for both restricted (RBM) and general Boltzmann machines (BM). These methods rely on the fidelity of samples from those devices, which approximate the characteristic Boltzmann distribution of the BM models. The models and optimization functions are built on top of the PyTorch and D-Wave Ocean libraries. The goal of this paper is to introduce developers and researchers to a familiar, yet flexible, software development framework, to explore the use of quantum computing in machine learning applications. The framework is open-source and has been made publicly available.

DOI
10.1109/qce60285.2024.00197

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This paper describes the components and configurations available in a new quantum-assisted machine learning (QAML) framework. QAML is an open source package that provides a new and flexible test-bed for algorithms to train and evaluate Boltzmann machines (BMs) using quantum annealers. Quantum annealing processors enable the training capabilities for both restricted (RBM) and general Boltzmann machines (BM). These methods rely on the fidelity of samples from those devices, which approximate the characteristic Boltzmann distribution of the BM models. The models and optimization functions are built on top of the PyTorch and D-Wave Ocean libraries. The goal of this paper is to introduce developers and researchers to a familiar, yet flexible, software development framework, to explore the use of quantum computing in machine learning applications. The framework is open-source and has been made publicly available.
We present a Hybrid-Quantum-classical method for learning Boltzmann machines (BM) for generative and discriminative tasks. Boltzmann machines are undirected graphs that form the building block of many learning architectures such as Restricted Boltzmann machines (RBM's) and Deep Boltzmann machines (DBM's). They have a network of visible and hidden nodes where the former are used as the reading sites while the latter are used to manipulate the probability of the visible states. BM's are versatile machines that can be used for both learning distributions as a generative task as well as for performing classification or function approximation as a discriminative task. We show that minimizing KL-divergence works best for training BM for applications of function approximation. In our approach, we use Quantum annealers for sampling Boltzmann states. These states are used to approximate gradients in a stochastic gradient descent scheme. The approach is used to demonstrate logic circuits in the discriminative sense and a specialized two-phase distribution using generative BM.
Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.
The Quantum Annealer built by D-Wave, known as Advantage, is currently the largest quantum computer in the world, featuring a topology called “Pegasus.” This groundbreaking system opens new possibilities for solving highly complex problems. The advancement of quantum annealers has spurred experimental demonstrations and intensified research interest, particularly in quantum machine learning. However, the application of quantum annealing in machine learning remains limited due to the lack of conclusive performance evaluations on real-world datasets. There is still no clear consensus on the efficacy of these models in practical scenarios. This work focuses on experimentally evaluating quantum annealing machine learning (QAML) classification methods, specifically Quantum Support Vector Machines (QSVM) and QBoost, on ADMET datasets—one of the most important datasets in the drug discovery domain. We compare QAML with classical machine learning to evaluate their relative performance. This study seeks to address this gap by rigorously comparing the performance of QBoost and QSVM models using ADMET datasets, employing D-Wave’s Quantum Annealer. This work provides a comprehensive analysis of the potential and limitations of quantum annealers in quantum machine learning, with a focus on their application to real-world data in the ADMET domain. The findings offer critical insights into the nuanced advantages and challenges of quantum annealers in advancing machine learning methodologies.
Motivated by the potential performance gains offered by quantum computing (QC), a recent research focus — known as quantum-assisted machine learning (QAML) — aims to develop machine learning algorithms tailored for execution on quantum computers while processing data that originate from a classical (i.e. non-quantum) phenomenon. QAML has been studied in various quantum computing (QC) paradigms. This paper, in particular, offers a brief overview of QAML within the context of adiabatic quantum computing (AQC). The major challenge in this case is to reformulate the machine learning task as a quadratic unconstrained binary optimization (QUBO) problem, which lies at the core of existing AQC physical implementations. We provide examples of machine learning techniques tailored to AQC, along with applications in remote sensing.
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of full Boltzmann machines and multi-layer, fully connected models and do not have well known classical counterparts.
Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we develop a quantum bayesian learning framework of the restricted Boltzmann machine in the quantum-enhanced feature spaces. Our framework provides the encoding phase to map the real data and Boltzmann weight onto the quantum feature spaces and the training phase to learn an optimal inference function. Specifically, the training phase provides a physical quantity to measure the posterior distribution in quantum feature spaces, and this measure is utilized to design the quantum maximum a posterior (QMAP) algorithm and the quantum predictive distribution estimator (QPDE). It is shown that both quantum algorithms achieve exponential speed-up over their classical counterparts. Furthermore, it is interesting to note that our framework can figure out the classical bayesian learning tasks, i.e. processing the classical data and outputting corresponding classical labels. And a simulation, which is performed on an open-source software framework for quantum computing, illustrates that our algorithms show almost the same classification performance compared to their classical counterparts. Noting that the proposed quantum algorithms utilize the shallow circuit, our work is expected to be implemented on the noisy intermediate-scale quantum (NISQ) devices, and is one of the promising candidates to achieve quantum supremacy.