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Communications Physics

Anomaly detection speed-up by quantum restricted Boltzmann machines

Lorenzo Moro, Enrico Prati

Published Sep 23, 2023• 23 citations
Publisher

Abstract

Abstract Quantum machine learning promises to revolutionize traditional machine learning by efficiently addressing hard tasks for classical computation. While claims of quantum speed-up have been announced for gate-based quantum computers and photon-based boson samplers, demonstration of an advantage by adiabatic quantum annealers (AQAs) is open. Here we quantify the computational cost and the performance of restricted Boltzmann machines (RBMs), a widely investigated machine learning model, by classical and quantum annealing. Despite the lower computational complexity of the quantum RBM being lost due to physical implementation overheads, a quantum speed-up may arise as a reduction by orders of magnitude of the computational time. By employing real-world cybersecurity datasets, we observe that the negative phase on sufficiently challenging tasks is computed up to 64 times faster by AQAs during the exploitation phase. Therefore, although a quantum speed-up highly depends on the problem’s characteristics, it emerges in existing hardware on real-world data.

DOI
10.1038/s42005-023-01390-y

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Abstract Quantum machine learning promises to revolutionize traditional machine learning by efficiently addressing hard tasks for classical computation. While claims of quantum speed-up have been announced for gate-based quantum computers and photon-based boson samplers, demonstration of an advantage by adiabatic quantum annealers (AQAs) is open. Here we quantify the computational cost and the performance of restricted Boltzmann machines (RBMs), a widely investigated machine learning model, by classical and quantum annealing. Despite the lower computational complexity of the quantum RBM being lost due to physical implementation overheads, a quantum speed-up may arise as a reduction by orders of magnitude of the computational time. By employing real-world cybersecurity datasets, we observe that the negative phase on sufficiently challenging tasks is computed up to 64 times faster by AQAs during the exploitation phase. Therefore, although a quantum speed-up highly depends on the problem’s characteristics, it emerges in existing hardware on real-world data.
Anomaly detection in Endpoint Detection and Response (EDR) is a critical task in cybersecurity programs of large companies. With rapidly growing amounts of data and the omnipresence of zero-day attacks, manual and rule-based detection techniques are no longer eligible in practice. While classical machine learning approaches to this problem exist, they frequently show unsatisfactory performance in differentiating malicious from benign anomalies. A promising approach to attain superior generalization than currently employed machine learning techniques are quantum generative models. Allowing for the largest representation of data on available quantum hardware, we investigate Quantum Annealing based Quantum Boltzmann Machines (QBMs) for the given problem. We contribute the first fully unsupervised approach for the problem of anomaly detection using QBMs and evaluate its performance on an EDR inspired synthetic dataset. Our results indicate that QBMs can outperform their classical analog (i.e., Restricted Boltzmann Machines) in terms of result quality and training steps in special cases. When employing Quantum Annealers from D-Wave Systems, we conclude that either more accurate classical simulators or substantially more QPU time is needed to conduct the necessary hyperparameter optimization allowing to replicate our simulation results on quantum hardware.
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.
Restricted Boltzmann machines are common machine learning models that can utilize quantum annealing devices in their training processes as quantum samplers. While this approach has shown promise as an alternative to classical sampling methods, the limitations of quantum annealing hardware, such as the number of qubits and the lack of connectivity between the qubits, still pose a barrier to wide-scale adoption. We propose the use of multiple software techniques such as dropout method, passive labeling, and parallelization techniques for addressing these hardware limitations. The study found that using these techniques along with quantum sampling showed comparable results to its classical counterparts in certain contexts, while in others the increased complexity of the sampling process hindered the performance of the trained models. This means that further research into the behavior of quantum sampling needs to be done to apply quantum annealing to training tasks of more complicated RBM models.
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.
Use cases for emerging quantum computing platforms become economically relevant as the efficiency of processing and availability of quantum computers increase. We assess the performance of Restricted Boltzmann Machines (RBM) assisted by quantum computing, running on real quantum hardware and simulators, using a real dataset containing 145 million transactions provided by Stone, a leading Brazilian fintech, for credit card fraud detection. The results suggest that the quantum-assisted RBM method is able to achieve superior performance in most figures of merit in comparison to classical approaches, even using current noisy quantum annealers. Our study paves the way for implementing quantum-assisted RBMs for general fault detection in financial systems.
Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from real-world applications is one of the key milestones towards a quantum ready era. Here, we take a first step towards addressing this challenge by performing a comparison of the widely used classical ML models known as restricted Boltzmann machines (RBMs), against a recently proposed quantum model, now known as quantum circuit Born machines (QCBMs). Both models address the same hard tasks in unsupervised generative modeling, with QCBMs exploiting the probabilistic nature of quantum mechanics and a candidate for near-term quantum computers, as experimentally demonstrated in three different quantum hardware architectures to date. To address the question of the performance of the quantum model on real-world classical data sets, we construct scenarios from a probabilistic version out of the well-known portfolio optimization problem in finance, by using time-series pricing data from asset subsets of the S&P500 stock market index. It is remarkable to find that, under the same number of resources in terms of parameters for both classical and quantum models, the quantum models seem to have superior performance on typical instances when compared with the canonical training of the RBMs. Our simulations are grounded on a hardware efficient realization of the QCBMs on ion-trap quantum computers, by using their native gate sets, and therefore readily implementable in near-term quantum devices.