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arXiv:2409.05475

Reinforcement Learning for Variational Quantum Circuits Design

Simone Foderà, Gloria Turati, Riccardo Nembrini, Maurizio Ferrari Dacrema, Paolo Cremonesi

Published Sep 9, 2024• 1 citation
arXivHTMLPDF

Abstract

Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. These algorithms leverage a parametric quantum circuit called ansatz, where its parameters are adjusted by a classical optimizer with the goal of optimizing a certain cost function. However, a significant challenge lies in designing effective circuits for addressing specific problems. In this study, we leverage the powerful and flexible Reinforcement Learning paradigm to train an agent capable of autonomously generating quantum circuits that can be used as ansatzes in variational algorithms to solve optimization problems. The agent is trained on diverse problem instances, including Maximum Cut, Maximum Clique and Minimum Vertex Cover, built from different graph topologies and sizes. Our analysis of the circuits generated by the agent and the corresponding solutions shows that the proposed method is able to generate effective ansatzes. While our goal is not to propose any new specific ansatz, we observe how the agent has discovered a novel family of ansatzes effective for Maximum Cut problems, which we call $R_{yz}$-connected. We study the characteristics of one of these ansatzes by comparing it against state-of-the-art quantum algorithms across instances of varying graph topologies, sizes, and problem types. Our results indicate that the $R_{yz}$-connected circuit achieves high approximation ratios for Maximum Cut problems, further validating our proposed agent. In conclusion, our study highlights the potential of Reinforcement Learning techniques in assisting researchers to design effective quantum circuits which could have applications in a wide number of tasks.

DOI
10.48550/arxiv.2409.05475

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Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. These algorithms leverage a parametric quantum circuit called ansatz, where its parameters are adjusted by a classical optimizer with the goal of optimizing a certain cost function. However, a significant challenge lies in designing effective circuits for addressing specific problems. In this study, we leverage the powerful and flexible Reinforcement Learning paradigm to train an agent capable of autonomously generating quantum circuits that can be used as ansatzes in variational algorithms to solve optimization problems. The agent is trained on diverse problem instances, including Maximum Cut, Maximum Clique and Minimum Vertex Cover, built from different graph topologies and sizes. Our analysis of the circuits generated by the agent and the corresponding solutions shows that the proposed method is able to generate effective ansatzes. While our goal is not to propose any new specific ansatz, we observe how the agent has discovered a novel family of ansatzes effective for Maximum Cut problems, which we call RyzR_{yz}Ryz​-connected. We study the characteristics of one of these ansatzes by comparing it against state-of-the-art quantum algorithms across instances of varying graph topologies, sizes, and problem types. Our results indicate that the RyzR_{yz}Ryz​-connected circuit achieves high approximation ratios for Maximum Cut problems, further validating our proposed agent. In conclusion, our study highlights the potential of Reinforcement Learning techniques in assisting researchers to design effective quantum circuits which could have applications in a wide number of tasks.
As quantum computing continues to gain attention, there is growing interest in how classical machine learning can assist quantum workflows in practice. Automated circuit design, sometimes referred to as Quantum Architecture Search (QAS), is a natural application but relies on the ability to model the quantum system to support learning as the number of qubits grows. This challenge is central to QAS, and much of the current literature that proposes new ways to model the ansatz focuses on small systems, often around ten qubits. In this work, we propose a complementary approach that separates a small-scale structure discovery phase, where a reusable modular circuit block is learned on small instances where classical learning is feasible, from a deployment phase, where the blocks are used to create the ansatz required for larger problems. To this end, we introduce Reinforcement Learning for Variational Quantum Circuits (RLVQC), formulating QAS as a sequential decision-making problem. We evaluate our methodology on Quadratic Unconstrained Binary Optimization (QUBO) instances derived from Maximum Cut, Maximum Clique, and Minimum Vertex Cover. Our RLVQC Block model is trained to discover a modular two-qubit block that can generalize QAOA-style methods and that is often beneficial compared to learning non-modular ansatzes. The blocks discovered on n=8 instances remain effective when deployed on larger instances (n=12 and n=16), supporting the feasibility of reusing learned modular structure across problem sizes. While we do not aim to establish a new state-of-the-art solver or an advantage over classical methods, our results provide evidence that modular ansatz structure can be learned on smaller instances and then extended to larger ones without requiring learning on systems with a large number of qubits, where quantum computing becomes interesting but classical computation becomes impractical.
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.
Quantum chemistry and optimization are two of the most prominent applications of quantum computers. Variational quantum algorithms have been proposed for solving problems in these domains. However, the design of the quantum circuit ansatz remains a challenge. Of particular interest is developing a method to generate circuits for any given instance of a problem, not merely a circuit tailored to a specific instance of the problem. To this end, we present a reinforcement learning (RL) approach to learning a problem-dependent quantum circuit mapping, which outputs a circuit for the ground state of a Hamiltonian from a given family of parameterized Hamiltonians. For quantum chemistry, our RL framework takes as input a molecule and a discrete set of bond distances, and it outputs a bond-distance-dependent quantum circuit for arbitrary bond distances along the potential energy curve. The inherently non-greedy approach of our RL method contrasts with existing greedy approaches to adaptive, problem-tailored circuit constructions. We demonstrate its effectiveness for the four-qubit and six-qubit lithium hydride molecules, as well as an eight-qubit H4_44​ chain. Our learned circuits are interpretable in a physically meaningful manner, thus paving the way for applying RL to the development of novel quantum circuits for the ground states of large-scale molecular systems.
We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate the versatility of the agent by incorporating additional optimization routines on the workflow during training, improving the two-qubit gate count state-of-the-art on multiple structured quantum circuits for relevant applications of much larger dimension and different gate distributions than the circuits the agent trains on. This conveys the potential of tailoring the reward function to the specific characteristics of each application and hardware backend. Our approach is a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ).
Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables a stable single-player version of self-play training and helps the agent escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.
A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an εεε-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.