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).
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 computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy intermediate-scale quantum hardware. To advance towards more reliable quantum computing, we introduce a framework based on ZX calculus, graph-neural networks and reinforcement learning for quantum circuit optimization. By combining reinforcement learning and tree search, our method addresses the challenge of selecting optimal sequences of ZX calculus rewrite rules. Instead of relying on existing heuristic rules for minimizing circuits, our method trains a novel reinforcement learning policy that directly operates on ZX-graphs, therefore allowing us to search through the space of all possible circuit transformations to find a circuit significantly minimizing the number of CNOT gates. This way we can scale beyond hard-coded rules towards discovering arbitrary optimization rules. We demonstrate our method's competetiveness with state-of-the-art circuit optimizers and generalization capabilities on large sets of diverse random circuits.
The practical implementation of quantum algorithms on noisy intermediate-scale quantum devices encounters operational limitations due to decoherence and other sources of noise inherent in real hardware. To mitigate these errors while preserving the original functionality of the algorithm, shorter quantum circuits are therefore preferred. This motivates the development of effective quantum circuit optimization algorithms. Learning-based approaches have emerged as a leading candidate, yet existing autonomous agents remain inefficient, spending most of their training capacity rediscovering elementary reductions that deterministic rule-based methods already handle reliably. To address this challenge, we propose a reinforcement learning framework that embeds a deterministic Commutation-and-Reduction (CR) algorithm directly into the training environment. After every agent action, the CR algorithm automatically resolves elementary commutations and cancellations, enabling the agent to focus its learning capacity on the non-trivial optimizations where reinforcement learning adds real value. Empirical evaluation across two gate sets, the universal Clifford+T basis and the CNOT+Pauli basis, shows that RL+CR produces shorter circuits than a standard RL agent at all tested scales. We demonstrate that RL trained on smaller quantum circuits can be applied to larger quantum circuits. On 20-qubit Clifford+T circuits, five times larger than the training circuits, RL+CR removes twice as many gates as standard RL. This work provides a robust approach that could accelerate the compilation and optimization processes for future fault-tolerant and utility-scale quantum systems.
This paper presents a novel approach to quantum circuit compilation leveraging reinforcement learning (RL). The core idea is to train an RL agent to dynamically optimize quantum circuit structures, aiming to minimize gate count and enhance overall circuit performance. Traditional quantum circuit compilation methods often rely on static heuristics and pre-defined optimization strategies, which may not be optimal for all quantum algorithms or hardware platforms. Our approach addresses this limitation by allowing the RL agent to learn a policy that adapts to the specific characteristics of the algorithm and the target quantum hardware. The agent learns by interacting with a simulated quantum circuit environment, receiving rewards based on circuit fidelity, depth, and gate count. The results demonstrate the potential of RL to significantly improve the efficiency and robustness of quantum computations. The key components of the system are: a high-level quantum algorithm representation, an RL agent, a quantum circuit simulator, and a reward function. The agent's policy is represented as a neural network, enabling it to generalize across different algorithms and hardware. We demonstrate the effectiveness of this approach through simulations, showcasing its ability to outperform conventional compilation methods in terms of reducing circuit depth and gate count while maintaining high fidelity.
Abstract ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy, simulated annealing, and state-of-the-art hand-crafted algorithms. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.
In fault-tolerant quantum computing systems, the T gates consume more fault-tolerant resources. In this paper, we propose an automated optimization method based on the Proximal Policy Optimization (PPO) algorithm. We first translate quantum circuits into ZX-diagrams using ZX-calculus, transforming the circuit optimization problem into a graph rewriting task. Subsequently, the PPO agent, powered by graph neural networks (GNNs) to encode the complex graph structures of the ZX-diagrams, learns to predict efficient transformation paths by focusing on local node and edge features. The PPO algorithm ensures stable policy updates through its clipped objective function, which prevents excessively large and potentially detrimental changes during optimization. Experimental results confirm the method’s effectiveness, showing an average reduction in T-count of 3.12% compared to the baseline approach.
Quantum computing promises significant computational advantages over classical methods in certain applications but is currently too unstable for executing complex tasks. High-fidelity quantum circuits are critical to overcoming this challenge, yet they are computationally challenging to design. On current noisy intermediate-scale quantum (NISQ) hardware, shallower circuits with fewer two-qubit gates generally run with higher fidelity. Increased fidelity can be sought by sequentially rewriting the circuit, which involves a vast search space. This costly search space exploration could be circumvented by using reinforcement learning (RL) to teach an agent to rewrite the circuit in a sequential decision-making process. This thesis aims to implement a Deep Q-Network (DQN) algorithm to optimize BernsteinVazirani (BVZ) circuits. The DQN algorithm interacts with a Cirq-based environment. The environment provides valid rewrite actions to the DQN algorithm, which gains a scalar reward emphasizing depth and gate reduction. In the thesis we compare two different state encodings as input for the neural network: a compact state summarizing vector representation with three features, and an image-like encoding that maps circuit state topology with tokens through a fixed embedding. Both input encodings use the same action rewrite set and reward design. The network is implemented in PyTorch and trained with Adam optimizer, and runs on GPU via CUDA. Empirically, the agent shows promising initial optimizing performance. On several BVZ circuits with varying qubit count and topology, the agent drives the depth toward the theoretical optimum of three. The simplistic vector encoding already reaches reasonable circuit depth plateaus, with the image-like encoding together with hyperparameter tuning improving reliability, showing avenues for continued improvement. We conclude that DQN is a viable foundation for automated circuit optimization on BVZ circuits. To achieve reliable circuit optimization at scale, future research should investigate even richer encoding methods and reward function shaping. Finally, the results support applying the DQN to be applied to circuit families beyond BVZ.