  Existing numerical optimizers deployed in quantum compilers use expensive
$\mathcal{O}(4^n)$ matrix-matrix operations. Inspired by recent advances in
quantum machine learning (QML), QFactor-Sample replaces matrix-matrix
operations with simpler $\mathcal{O}(2^n)$ 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.
