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Optimizing Quantum Annealing Schedules: From Monte Carlo Tree Search to QuantumZero

Yuqin Chen, Yu Chen, Chee‐Kong Lee, Shengyu Zhang, Chang‐Yu Hsieh

Published Apr 6, 2020• 4 citations
OpenAlex

Abstract

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.

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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.
One of the key research focuses in quantum annealing is the design and optimization of annealing schedules to enhance computational efficiency, enabling large-scale applications. QuantumZero (QZero) pioneered the integration of Monte Carlo Tree Search (MCTS) with neural networks to autonomously design annealing schedules within a hybrid quantum-classical framework. This approach is distinguished by its ability to enhance the performance of Monte Carlo Tree Search through the integration of neural networks, enabling the efficient design of annealing paths even with limited annealing time. The paper presents an optimized QZero method based on intuitive reasoning theory and MindSpore, which further enhances QZero's ability to conserve computational resources and resist noise. In terms of learning efficiency, the optimized QZero algorithm improves the convergence speed of the neural network by 93% compared to the original algorithm. Notably, the average number of quantum annealing queries required to achieve 99% fidelity is reduced by 45.09%. Regarding noise resistance, the optimized QZero algorithm requires 34.27% fewer quantum annealing queries to reach 990% fidelity compared to the original algorithm. The optimized QZero algorithm demonstrates strong competitiveness in optimizing quantum annealing schedules.
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.
The process of designing optimal deep neural network architectures is a computationally expensive and often manual task. Traditional gradient-based optimization methods struggle to efficiently explore the vast architectural search space, leading to sub-optimal designs. This research proposes a novel approach leveraging quantum-inspired optimization techniques, specifically quantum annealing, to accelerate the architecture search process. We formulate the architecture search problem as a minimization task within a quantum annealing landscape. The objective function is designed to reflect the performance metrics of a given neural network architecture. Our approach offers a potentially more efficient method for discovering high-performing architectures by harnessing the principles of quantum mechanics, particularly superposition and tunneling, to navigate the complex search space. The core claim is that gradient-based optimization is often inefficient for this task, and quantum annealing provides a viable alternative. This paper outlines the theoretical framework and proposes an initial methodology for applying quantum annealing to deep neural network architecture search.
This paper presents an adaptive quantum annealing algorithm designed to improve the performance of quantum annealing in solving combinatorial optimization problems. Traditional quantum annealing relies on a fixed annealing schedule, which may not be optimal for all problems. This work introduces a novel approach that utilizes reinforcement learning to dynamically adjust the annealing parameters during the annealing process, based on the observed progress towards a solution. The algorithm learns an optimal annealing schedule by interacting with the quantum annealing system, maximizing the probability of finding a good solution within a given time limit. We demonstrate the theoretical framework and outline the core components of the adaptive algorithm, highlighting its potential advantages over conventional fixed-schedule quantum annealing. The key performance metric is the solution quality (e.g., objective function value) achieved after annealing. The algorithm's effectiveness is evaluated through conceptual analysis and design considerations. This approach aims to bridge the gap between the theoretical potential of quantum annealing and its practical application in solving real-world combinatorial optimization challenges.
The design of deep neural network (DNN) architectures is a complex and computationally intensive task. Traditional methods often rely on manual tuning or random search, which are inefficient in exploring the exponentially large architectural space. This paper proposes a novel approach to DNN architecture optimization leveraging quantum-inspired algorithms. Specifically, we explore the application of algorithms inspired by quantum annealing and quantum Monte Carlo methods to efficiently search for optimal DNN configurations. Our framework aims to minimize the trade-off between accuracy, latency, and energy consumption – key considerations in real-world DNN deployments. We present a theoretical framework and outline a methodology for integrating these quantum-inspired techniques. The core idea is to map the architectural design problem onto a suitable quantum system, allowing for the parallel exploration of potential solutions. This research provides a new direction for automated DNN design, potentially leading to significant improvements in performance and efficiency.
The standard quantum annealing algorithm tries to approach the ground state of a classical system by slowly decreasing the hopping rates of a quantum random walk in the configuration space of the problem, where the on-site energies are provided by the classical energy function. In a quantum reinforcement algorithm, the annealing works instead by increasing gradually the strength of the on-site energies according to the probability of finding the walker on each site of the configuration space. Here, by using the path-integral Monte Carlo simulations of the quantum algorithms, we show that annealing via reinforcement can significantly enhance the success probability of the quantum walker. More precisely, we implement a local version of the quantum reinforcement algorithm, where the system wave function is replaced by an approximate wave function using the local expectation values of the system. We use this algorithm to find solutions to a prototypical constraint satisfaction problem (XORSAT) close to the satisfiability to unsatisfiability phase transition. The study is limited to small problem sizes (a few hundreds of variables), nevertheless, the numerical results suggest that quantum reinforcement may provide a useful strategy to deal with other computationally hard problems and larger problem sizes even as a classical optimization algorithm.