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arXiv:2211.15209 · New Journal of Physics

Deep learning optimal quantum annealing schedules for random Ising models

Pratibha Raghupati Hegde, Gianluca Passarelli, Giovanni Cantele, Procolo Lucignano

Published Jul 1, 2023• 12 citations
arXivHTMLPDF

Abstract

Abstract A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training.

DOI
10.1088/1367-2630/ace547

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Abstract A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training.
Quantum annealing is a practical approach to execute the native instruction set of the adiabatic quantum computation model. The key of running adiabatic algorithms is to maintain a high success probability of evolving the system into the ground state of a problem-encoded Hamiltonian at the end of an annealing schedule. This is typically done by executing the adiabatic algorithm slowly to enforce adiabacity. However, properly optimized annealing schedule can accelerate the computational process. Inspired by the recent success of DeepMind's AlphaZero algorithm that can efficiently explore and find a good winning strategy from a large combinatorial search with a neural-network-assisted Monte Carlo Tree Search (MCTS), we adopt MCTS and propose a neural-network-enabled version, termed QuantumZero (QZero), to automate the design of an optimal annealing schedule in a hybrid quantum-classical framework. The flexibility of having neural networks allows us to apply transfer-learning technique to boost QZero's performance. We find both MCTS and QZero to perform very well in finding excellent annealing schedules even when the annealing time is short in the 3-SAT examples we consider in this study. We also find MCTS and QZero to be more efficient than many other leading reinforcement leanring algorithms for the task of desining annealing schedules. In particular, if there is a need to solve a large set of similar problems using a quantum annealer, QZero is the method of choice when the neural networks are first pre-trained with examples solved in the past.
Quantum-assisted optimization of neural network architecture is a burgeoning field aiming to accelerate the design and training of deep learning models. This paper explores the application of quantum annealing to this domain, proposing a novel algorithm that leverages quantum phenomena to efficiently explore the vast parameter space of neural network architectures. We detail the core mechanism, highlighting the unique advantages of quantum annealing in tackling the inherent complexities of neural network design. The paper presents a comprehensive analysis of the theoretical underpinnings, experimental validation, and potential future directions of this research. The core claim is that quantum annealing can significantly improve the performance and efficiency of neural network architectures compared to classical optimization methods, particularly in complex scenarios.
This paper investigates the application of quantum annealing to the combinatorial optimization problem inherent in neural network training, specifically focusing on hyperparameter tuning. Traditional methods for hyperparameter optimization, such as grid search and random search, can be computationally expensive and often fail to efficiently explore the vast hyperparameter space. We propose a novel approach that maps the hyperparameter optimization task onto a quantum annealing landscape. The quantum annealer, leveraging quantum tunneling, is then utilized to navigate this landscape and identify optimal hyperparameter values. This approach aims to accelerate the training process and enhance the performance of neural networks. The core concept involves formulating the hyperparameter tuning problem as an Ising model, which can be directly implemented on quantum annealing hardware. We explore the theoretical underpinnings of this mapping and discuss the potential advantages and limitations of this method. The results, although not based on experimental validation due to the nature of the research, demonstrate a promising trajectory for integrating quantum computing with machine learning. Further research and development are required to fully realize the potential of this approach.
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been profoundly successful in pushing the boundaries of AI. It is thus natural to investigate potentially game changing technologies such as quantum annealers to augment the capabilities of deep learning. In this work, we explore binary neural networks, which are lightweight yet powerful models typically intended for resource constrained devices. Departing from current training regimes for binary networks that smooth/approximate the activation functions to make the network differentiable, we devise a quadratic unconstrained binary optimization formulation for the training problem. While the problem is intractable, i.e., the cost to estimate the binary weights scales exponentially with network size, we show how the problem can be optimized directly on a quantum annealer, thereby opening up to the potential gains of quantum computing. We experimentally validated our formulation via simulation and testing on an actual quantum annealer (D-Wave Advantage), the latter to the extent allowable by the capacity of current technology.
Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredients: binary encoding the free parameters of the network; polynomial approximation of the activation function; and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. After training the network using a quantum annealer, one can then use the quantum network weights in a classical network algorithm of identical design for inference. Our approach opens an avenue for the quantum training of general machine learning models.
Variational neural network models have achieved remarkable success in solving ground-state problems of quantum many-body systems. However, addressing classical and quantum spin glasses remains challenging, as disorder and energy frustration give rise to an exponentially large number of local energy minima separated by high-energy barriers, hindering the efficiency of conventional Metropolis-based Monte Carlo methods. To bridge this gap, we introduce Deep Boltzmann Quantum States, a class of neural quantum states inspired by deep Boltzmann machines that inherit efficient block Gibbs sampling. We also propose two key advances in the training algorithm. Firstly, we combine natural-gradient updates with state-of-the-art stochastic optimizers. Secondly, we gradually tune the hardness of the problem Hamiltonian by interpolating from an easy to a hard regime, without the need to closely approximate the instantaneous adiabatic state at intermediate times. We match the exact solution or the best available estimate for several instances of classical and quantum Ising spin-glass models with infinite-range interactions and hundreds of spins. We also solve instances of the NP-hard Job Shop Scheduling Problem exceeding the current limitations of quantum annealing hardware. To summarize, deep neural architectures with efficient global update rules and trained within an annealing-like scheme, provide a powerful framework for solving real-world hard combinatorial optimization and for investigating disordered quantum many-body systems.