Optimizing quantum circuit placement via machine learning

Quantum circuit placement (QCP) is the process of mapping the synthesized logical quantum programs on physical quantum machines, which introduces additional SWAP gates and affects the performance of quantum circuits. Nevertheless, determining the minimal number of SWAP gates has been demonstrated to be an NP-complete problem. Various heuristic approaches have been proposed to address QCP, but they suffer from suboptimality due to the lack of exploration. Although exact approaches can achieve higher optimality, they are not scalable for large quantum circuits due to the massive design space and expensive runtime. By formulating QCP as a bilevel optimization problem, this paper proposes a novel machine learning (ML)-based framework to tackle this challenge. To address the lower-level combinatorial optimization problem, we adopt a policy-based deep reinforcement learning (DRL) algorithm with knowledge transfer to enable the generalization ability of our framework. An evolutionary algorithm is then deployed to solve the upper-level discrete search problem, which optimizes the initial mapping with a lower SWAP cost. The proposed ML-based approach provides a new paradigm to overcome the drawbacks in both traditional heuristic and exact approaches while enabling the exploration of optimality-runtime trade-off. Compared with the leading heuristic approaches, our ML-based method significantly reduces the SWAP cost by up to 100%. In comparison with the leading exact search, our proposed algorithm achieves the same level of optimality while reducing the runtime cost by up to 40 times.