QFactor-Sample: Leveraging Quantum Machine Learning Generalization to Significantly Speed-up Quantum Compilation

Existing numerical optimizers deployed in quantum compilers use expensive O(4^n) matrix-matrix operations. Inspired by recent advances in quantum machine learning (QML), QFactor-Sample replaces matrix-matrix operations with simpler O(2^n) circuit simulations on a set of sample inputs. The simpler the circuit, the lower the number of required input samples. We validate QFactor-Sample on a large set of circuits and discuss its hyperparameter tuning. When incorporated in the BQSKit quantum compiler and compared against a state-of-the-art domain-specific optimizer, We demonstrate improved scalability and a reduction in compile time, achieving an average speedup factor of 69 for circuits with more than 8 qubits. We also discuss how improved numerical optimization affects the dynamics of partitioning-based compilation schemes, which allow a trade-off between compilation speed and solution quality.