Abstract The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum–classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.
Abstract The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum–classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.
Variational quantum algorithms stand at the forefront of simulations on near-term and future fault-tolerant quantum devices. While most variational quantum algorithms involve only continuous optimization variables, the representational power of the variational ansatz can sometimes be significantly enhanced by adding certain discrete optimization variables, as is exemplified by the generalized quantum approximate optimization algorithm (QAOA). However, the hybrid discrete-continuous optimization problem in the generalized QAOA poses a challenge to the optimization. We propose a new algorithm called MCTS-QAOA, which combines a Monte Carlo tree search method with an improved natural policy gradient solver to optimize the discrete and continuous variables in the quantum circuit, respectively. We find that MCTS-QAOA has excellent noise-resilience properties and outperforms prior algorithms in challenging instances of the generalized QAOA.
This paper investigates the potential of quantum computing to significantly enhance the efficiency of Monte Carlo Tree Search (MCTS) algorithms. MCTS, a cornerstone of modern artificial intelligence, particularly in game playing, relies heavily on computationally intensive simulations to evaluate game states and guide the search process. We propose a hybrid quantum-classical algorithm that leverages quantum superposition and entanglement to achieve a parallel exploration of the vast search space inherent in MCTS. The core mechanism involves utilizing quantum computers for specific tasks within the MCTS workflow, primarily the evaluation of game states. We formulate the problem as a quantum optimization task, mapping the state evaluation to a quantum objective function. The algorithm employs a classical controller to manage the quantum computation, orchestrating the simulations and extracting information. Preliminary theoretical analysis suggests a potential exponential speedup in state evaluation compared to classical simulations, contingent on the quality of the quantum hardware and the effectiveness of the hybrid approach. This research contributes to the broader field of quantum-accelerated AI and provides a framework for future investigations into the practical application of quantum computing within complex decision-making algorithms.
This paper explores the potential of quantum computing to revolutionize Monte Carlo Tree Search (MCTS) algorithms, a cornerstone technique in reinforcement learning and game AI. The core claim is that by harnessing quantum superposition and interference, we can significantly accelerate MCTS's exploration of complex optimization landscapes. The proposed approach utilizes quantum circuits to represent and evaluate game states, leveraging quantum parallelism to concurrently assess multiple branches of the search tree. We demonstrate, through theoretical analysis and algorithmic design, how this quantum-enhanced MCTS can outperform classical MCTS in scenarios with high computational complexity and vast search spaces. The resulting system offers a novel approach to solving complex optimization problems, particularly those found in areas such as game playing, portfolio optimization, and drug discovery. The presented methodology focuses on the conceptual framework and provides a roadmap for future research and development, emphasizing the integration of quantum hardware with sophisticated reinforcement learning strategies. The key innovation lies in the efficient mapping of the MCTS search process onto a quantum computing architecture, exploiting quantum mechanics to dramatically reduce the search time.
Over the past decades, the operations research community has developed numerous effective optimization algorithms, yet quantum computing is emerging as a new computational paradigm with the potential to approach optimization problems more efficiently. Grover's algorithm offers a provable speedup for combinatorial optimization, but its circuit depth places it beyond current noisy intermediate-scale quantum (NISQ) devices. A more accessible alternative is to reformulate the optimization problem as a quadratic unconstrained binary optimization (QUBO) problem and apply quantum annealing; however, practical problem instances remain out of reach for existing hardware. We introduce AtomTreeSearch, a hybrid classical-quantum algorithm that integrates a quantum subroutine natively implementable on neutral-atom quantum computers within a Monte Carlo Tree Search framework. At each expansion step, a maximal weighted independent set of candidate actions provided by the quantum processor is selected, and these collective actions are performed to obtain a child node. We benchmark our method on the Traveling Salesman Problem, with instances of up to 60 cities on random Euclidean instances and up to 100 cities on TSPLIB instances. Our hybrid algorithm generally matches or outperforms both OR-Tools and simulated annealing on these instances, and we find that the quantum subroutine produces more diverse and higher-quality branches compared to classical alternate subroutines. These results suggest that carefully scoped quantum subroutines embedded in classical search frameworks represent a promising path toward near-term quantum utility in combinatorial optimization.
Variational quantum algorithms (VQAs) hold significant promise for solving complex optimization problems in quantum computing. However, existing VQA approaches often suffer from premature convergence, struggling to effectively explore the high-dimensional optimization landscape and frequently settling into local minima. This paper introduces a novel strategy, Variational Quantum Evolution (VQE), designed to overcome these limitations. VQE utilizes a quantum-classical hybrid approach, continuously evolving the parameters of a quantum circuit through a simulated stochastic evolutionary process. A quantum process operator is employed to generate a range of quantum states, while a classical feedback loop, informed by the quantum measurements, dynamically adjusts the circuit parameters to promote exploration and escape local optima. The core innovation lies in integrating quantum evolution directly within the variational framework, harnessing quantum superposition and interference to drive a more robust and adaptive optimization trajectory. The proposed method offers a potential pathway to unlocking the full capabilities of VQAs by enabling a more thorough exploration of the solution space. We demonstrate, theoretically, the advantages of this approach and outline the key components required for its implementation.
Hybrid Quantum–Classical Optimization combines the advantages of quantum computing and classical optimization to address complex combinatorial optimization problems. The Quantum Approximate Optimization Algorithm (QAOA), as an outstanding Variational Quantum Algorithm (VQA), shows great potential in solving combinatorial optimization problems. Classical optimization methods play a crucial role in tuning the parameters of quantum circuits, affecting the algorithm’s convergence speed and solution quality. This paper designs and simulates QAOA circuits based on the Qiskit framework, focusing on comparing the performance of three classical optimizers— Adaptive Moment Estimation (Adam), Constrained Optimization BY Linear Approximations (COBYLA), and Simultaneous Perturbation Stochastic Approximation (SPSA)—in parameter optimization. Adam and SPSA perform more stably in deeper circuits, making them suitable for high-dimensional parameter spaces, whereas COBYLA tends to get trapped in local optima and exhibits greater fluctuations under limited iterations. The results further highlight the importance of classical optimizer selection and hyperparameter tuning in enhancing the performance of hybrid quantum–classical optimization algorithms.