Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning (2405.13196v1)

Abstract: This paper demonstrates the integration of Reinforcement Learning (RL) into quantum transpiling workflows, significantly enhancing the synthesis and routing of quantum circuits. By employing RL, we achieve near-optimal synthesis of Linear Function, Clifford, and Permutation circuits, up to 9, 11 and 65 qubits respectively, while being compatible with native device instruction sets and connectivity constraints, and orders of magnitude faster than optimization methods such as SAT solvers. We also achieve significant reductions in two-qubit gate depth and count for circuit routing up to 133 qubits with respect to other routing heuristics such as SABRE. We find the method to be efficient enough to be useful in practice in typical quantum transpiling pipelines. Our results set the stage for further AI-powered enhancements of quantum computing workflows.

• The paper introduces an RL-based method for quantum circuit synthesis, achieving near-optimal results for 6-qubit Clifford circuits and reducing SWAP layers for permutation circuits.
• The RL approach enhances circuit routing by dynamically optimizing SWAP operations, cutting circuit depth by around 40% and reducing two-qubit gate counts by 10%.
• The methodology combines classical and quantum resources, offering a practical solution for real-world systems with complex connectivity constraints.

Practical and Efficient Quantum Circuit Synthesis and Transpiling with Reinforcement Learning

Introduction

Quantum computing is a rapidly developing field, inviting contributions from various domains like chemistry and AI. As quantum technologies advance, users can access quantum processors via the cloud, exploring how to leverage quantum computing for their goals. Quantum computing's future lies in hybrid systems combining classical CPUs and GPUs with multiple quantum processors (QPUs), enabling computations on the scale of tens of thousands of qubits.

Enter Reinforcement Learning (RL), an AI method poised to push the boundaries of quantum computing. In the article under discussion, the authors present an RL-based approach to enhance quantum circuit transpiling and optimization. By integrating RL, the approach achieves significant improvements over existing heuristic methods, offering near-optimal solutions at a fraction of the computational cost.

Let's dive deeper into the results and implications of employing RL in quantum circuit synthesis and routing.

Circuit Synthesis with Reinforcement Learning

RL for Circuit Synthesis

The authors propose using RL to tackle circuit synthesis, framing it as a sequential decision process. Essentially, this involves choosing the appropriate gates to apply at each step to transform an operator into its identity form, thereby constructing the desired quantum circuit. This method involves:

1. Operator Representation: The operator is represented in a specific format (e.g., Clifford tableau for Clifford circuits).
2. Training Phase: The RL agent is trained using a reward function emphasizing smaller gate counts and faster circuits.
3. Inference Phase: Post-training, the agent synthesizes circuits by selecting gates based on learned probabilities.

Numerical Results in Synthesis

Significant benchmarks demonstrate the efficacy of the proposed RL strategy. For instance, the RL approach achieved near-optimal results:

• Clifford Circuits: For 6-qubit Clifford circuits, RL methods performed almost as optimally as SAT solvers but in a fraction of the time.
• Permutation Circuits: For synthesizing permutation circuits, RL achieved a significant reduction in SWAP layers compared to heuristic methods like TokenSwapper for various topologies, including 8-L and 65-HH.

Circuit Routing with Reinforcement Learning

RL for Circuit Routing

Routing in quantum computing involves inserting SWAPs to make two-qubit operations conform to the device's qubit connectivity. The authors treat circuit routing as another sequential decision process, with the goal of minimizing the overall gate count and depth.

1. Candidate Routing Strategies:
   • Fixed-size RL Routing: Applicable for small circuits, encoding the entire circuit into a fixed-size matrix.
   • Generic RL Routing: Similar to SABRE but enhanced by RL to choose the best SWAPs dynamically.
2. Training and Inference: The RL model is trained against a reward structure that penalizes non-efficient routings, and during inference, it dynamically selects SWAPs to optimize the circuit.

Numerical Results in Routing

The RL-based routing also outperformed existing methods:

• 133-Qubit QV Circuits: When routing random 3-layer QV circuits, RL routing reduced circuit depth by around 40% and two-qubit gate counts by 10% compared to the Qiskit SDK's heuristic methods.
• EfficientSU2 Circuits: RL routing achieved minimal SWAP overhead, routing EfficientSU2 circuits to near-optimal configurations.

Discussion

This research highlights the potential of integrating RL into quantum circuit transpilation workflows. Here are some critical takeaways:

1. Efficiency: RL models yield near-optimal solutions for synthesis and routing tasks, significantly reducing computational costs.
2. Practicality: The approach is practical for real-world quantum computing environments, enhancing the Qiskit Transpiler Service by reducing the depth and count of CNOT gates.
3. Adaptability: The method adapts to different classes of circuits (Clifford, Permutation, Linear Function) and remains compatible with native device instruction sets and connectivity constraints.

Future Directions:

• Enhanced Methods: Exploring Monte Carlo Tree Search could make the RL approach even more efficient at exploring action spaces.
• Scalability: There's potential to scale the method to larger circuits, possibly training more efficient models as technology advances.
• Dynamic Circuits: Applying RL methods to dynamic circuits, which include non-unitary operations, is an exciting frontier.

Conclusion

Integrating RL into quantum circuit transpilation promises significant advancements in efficiency and performance. By offering near-optimal solutions at lower computational costs, this approach marks a substantial improvement over traditional methods. As the field of quantum computing evolves, continued exploration of AI's role, particularly RL, could unlock new potentials and optimize quantum workflows even further.