Abstract Despite the anticipated speed‐up of quantum computing, the achievement of a measurable advantage remains subject to ongoing debate. Adiabatic Quantum Computers (AQCs) are quantum devices designed to solve quadratic uncostrained binary optimization (QUBO) problems, but their intrinsic thermal noise can be leveraged to train computationally demanding machine learning algorithms such as the Boltzmann Machine (BM). Despite an asymptotic advantage is expected only for large networks, a limited quantum speed up can be already achieved on a small BM is shown, by exploiting parallel adiabatic computation. This approach exhibits a 8.6‐fold improvement in wall time on the Bars and Stripes dataset when compared to a parallelized classical Gibbs sampling method, which has never been outperformed before by quantum approaches.
Abstract Despite the anticipated speed‐up of quantum computing, the achievement of a measurable advantage remains subject to ongoing debate. Adiabatic Quantum Computers (AQCs) are quantum devices designed to solve quadratic uncostrained binary optimization (QUBO) problems, but their intrinsic thermal noise can be leveraged to train computationally demanding machine learning algorithms such as the Boltzmann Machine (BM). Despite an asymptotic advantage is expected only for large networks, a limited quantum speed up can be already achieved on a small BM is shown, by exploiting parallel adiabatic computation. This approach exhibits a 8.6‐fold improvement in wall time on the Bars and Stripes dataset when compared to a parallelized classical Gibbs sampling method, which has never been outperformed before by quantum approaches.
We demonstrate how to leverage thermal noise within an Adiabatic Quantum Computer (AQC) to train a complete Boltzmann Machine (BM). In contrast to previous implementations, our fully-connected BM includes hidden units and we sample both negative and positive statistics from the AQC. By training the network on a standard benchmark Bars and Stripes dataset, the maximally parallelized classical algorithm takes 11.4 times longer to reach the same likelihood as the quantum algorithm, indicating that AQCs may expedite BM training. The ability of AQCs to sample Boltzmann-distributed configurations quickly has the potential to impact BMs training as well as influence the field of stochastic machine learning.
Abstract Restricted Boltzmann machines (RBMs) constitute a class of neural networks for unsupervised learning with applications ranging from pattern classification to quantum state reconstruction. Despite the potential representative power, the diffusion of RBMs is quite limited since their training process proves to be hard. The advent of commercial adiabatic quantum computers (AQCs) raised the expectation that the implementations of RBMs on such quantum devices can increase the training speed with respect to conventional hardware. Here, the feasibility of a complete RBM on AQCs is demonstrated, thanks to an embedding that associates the nodes of the neural networks to virtual qubits. A semantic quantum search is implemented thanks to a reverse annealing schedule. Such an approach exploits more information from the training data, mimicking the behavior of the classical Gibbs sampling algorithm. The semantic training is shown to quickly raise the sampling probability of a subset of the set of the configurations. Even without a proper optimization of the annealing schedule, the RBM semantically trained achieves good scores on reconstruction tasks. The development of such techniques paves the way toward the establishment of a quantum advantage of adiabatic quantum computers, especially given the foreseen improvement of such hardware.
A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to [Formula: see text] speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric. The quantum approach used the D-Wave 2000Q adiabatic quantum computer, whereas the classical approach used a desktop workstation with an 8-core Intel i9 processor. As such, the results obtained in this work must be interpreted within the context of the specific hardware and software implementations of these machines.
Boltzmann Machines constitute a paramount class of neural networks for unsupervised learning and recommendation systems. Their bipartite version, called Restricted Boltzmann Machine (RBM), is the most developed because of its satisfactory trade-off between computability on classical computers and computational power. Though the diffusion of RBMs is quite limited as their training remains hard. Recently, a renewed interest has emerged as Adiabatic Quantum Computers (AQCs), which suggest a potential increase of the training speed with respect to conventional hardware. Due to the limited number of connections among the qubits forming the graph of existing hardware, associating one qubit per node of the neural network implies an incomplete graph. Thanks to embedding techniques, we developed a complete graph connecting nodes constituted by virtual qubits. The complete graph outperforms previous implementations based on incomplete graphs. Despite the fact that the learning rate per epoch is still slower with respect to a classical machine, the advantage is expected by the increase of number of nodes which impacts on the classical computational time but not on the quantum hardware based computation.
The advent of quantum computing holds the potential to revolutionize various fields by solving complex problems more efficiently than classical computers. Despite this promise, practical quantum advantage is hindered by current hardware limitations, notably the small number of qubits and high noise levels. In this study, we leverage adiabatic quantum computers to optimize Kolmogorov-Arnold Networks, a powerful neural network architecture for representing complex functions with minimal parameters. By modifying the network to use Bezier curves as the basis functions and formulating the optimization problem into a Quadratic Unconstrained Binary Optimization problem, we create a fixed-sized solution space, independent of the number of training samples. This strategy allows for the optimization of an entire neural network in a single training iteration in which, due to order of operations, a majority of the processing is done using a collapsed version of the training dataset. This inherently creates extremely fast training speeds, which are validated experimentally, compared to classical optimizers including Adam, Stochastic Gradient Descent, Adaptive Gradient, and simulated annealing. Additionally, we introduce a novel rapid retraining capability, enabling the network to be retrained with new data without reprocessing old samples, thus enhancing learning efficiency in dynamic environments. Experiments on retraining demonstrate a hundred times speed up using adiabatic quantum computing based optimization compared to that of the gradient descent based optimizers, with theoretical models allowing this speed up to be much larger! Our findings suggest that with further advancements in quantum hardware and algorithm optimization, quantum-optimized machine learning models could have broad applications across various domains, with initial focus on rapid retraining.
A constantly increasing number of parameters in modern machine learning models has become a significant bottleneck in their efficient training, resulting in a disproportionate consumption of resources, expressed in terms of energy and computational time. The vast majority of such resources are allocated to the training phase rather than the inference stage, leading to an inefficient process [1] , [2] , [3] . This study addresses this problem by introducing a quantum alternative for training machine learning models, formalized as a Quadratic Unconstrained Binary Optimization ( QUBO ) problem. Adiabatic quantum computers have shown promise in approximately solving certain NP -hard problems, such as QUBO , potentially offering speed advantages over classical computers in specific scenarios [ 4 , 5, [6] , [7] ]. Given that many machine learning problems are also NP -hard, adiabatic quantum computers could play a pivotal role in efficiently training machine learning models. Furthermore, inspired by the ones’ complement binary numeral system, this work includes the proposal of an efficient binary-to-decimal encoding, which improves data representation in the quantum context. A concrete implementation of a regression training problem on specific quantum hardware is also presented here, the results of which suggest that the adoption of quantum techniques in model training allows not only to address the problem of parameter explosion but also to offer promising prospects for significantly accelerate the training process by exploiting the unique properties of quantum computation.