On the optimality of quantum circuit initial mapping using reinforcement learning

Quantum circuit optimization is an inevitable task with the current noisy quantum backends. This task is considered non-trivial due to the varying circuits’ complexities in addition to hardware-specific noise, topology, and limited connectivity. The currently available methods either rely on heuristics for circuit optimization tasks or reinforcement learning with complex unscalable neural networks such as transformers. In this paper, we are concerned with optimizing the initial logical-to-physical mapping selection. Specifically, we investigate whether a reinforcement learning agent with simple scalable neural network is capable of finding a near-optimal logical-to-physical mapping, that would decrease as much as possible additional CNOT gates, only from a fixed-length feature vector. To answer this question, we train a Maskable Proximal Policy Optimization agent to progressively take steps towards a near-optimal logical-to-physical mapping on a 20-qubit hardware architecture. Our results show that our agent coupled with a simple routing evaluation is capable of outperforming other available reinforcement learning and heuristics approaches on 12 out of 19 test benchmarks, achieving geometric mean improvements of 2.2% and 15% over the best available related work and two heuristics approaches, respectively. Additionally, our neural network model scales linearly as the number of qubits increases.