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ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD)

Training and Meta-Training Binary Neural Networks with Quantum Computing

Abdulah Fawaz, Paul Klein, Sebastien Piat, Simone Severini B, Peter Mountney

Published Jul 25, 2019• 17 citations
Publisher

Abstract

Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network.

DOI
10.1145/3292500.3330953

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Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network.
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Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However, their training, architectural design, and hyperparameter tuning remain challenging as these involve multiple computationally expensive combinatorial optimization problems. Here we introduce quantum hypernetworks as a mechanism to train binary neural networks on quantum computers, which unify the search over parameters, hyperparameters, and architectures in a single optimization loop. Through classical simulations, we demonstrate that our approach effectively finds optimal parameters, hyperparameters and architectural choices with high probability on classification problems including a two-dimensional Gaussian dataset and a scaled-down version of the MNIST handwritten digits. We represent our quantum hypernetworks as variational quantum circuits, and find that an optimal circuit depth maximizes the probability of finding performant binary neural networks. Our unified approach provides an immense scope for other applications in the field of machine learning.
The training of neural networks (NNs) is a computationally intensive task requiring significant time and resources. This article presents a novel approach to NN training using adiabatic quantum computing (AQC), a paradigm that leverages the principles of adiabatic evolution to solve optimization problems. We propose a universal AQC method that can be implemented on gate quantum computers, allowing for a broad range of Hamiltonians and thus enabling the training of expressive neural networks. We apply this approach to various neural networks with continuous, discrete, and binary weights. The study results indicate that AQC can very efficiently evaluate the global minimum of the loss function, offering a promising alternative to classical training methods.
Quantum Machine Learning is an emerging sub-field in machine learning where one of the goals is to perform pattern recognition tasks by encoding data into quantum states. This extension from classical to quantum domain has been made possible due to the development of hybrid quantum-classical algorithms that allow a parameterized quantum circuit to be optimized using gradient based algorithms that run on a classical computer. The similarities in training of these hybrid algorithms and classical neural networks has further led to the development of Quantum Neural Networks (QNNs). However, in the current training regime for QNNs, the gradients w.r. t objective function have to be computed on the quantum device. This computation is highly non-scalable and is affected by hardware and sampling noise present in the current generation of quantum hardware. In this paper, we propose a training algorithm that does not rely on gradient information. Specifically, we introduce a novel meta-optimization algorithm that trains a meta-optimizer network to output parameters for the quantum circuit such that the objective function is minimized. We empirically and theoretically show that we achieve a better quality minima in fewer circuit evaluations than existing gradient based algorithms on different datasets.
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Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.