Leveraging Quantum Machine Learning Generalization to Significantly Speed up Quantum Compilation

Existing numerical optimizers deployed in quantum compilers use expensive <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(4^{n})$</tex-math></inline-formula> matrix–matrix operations. Inspired by recent advances in quantum machine learning, <inline-formula><tex-math notation="LaTeX">${\rm{QFactor}}$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">${\rm{Sample}}$</tex-math></inline-formula> replaces matrix–matrix operations with simpler <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(2^{n})$</tex-math></inline-formula> circuit simulations on a set of sample inputs. The simpler the circuit, the lower the number of required input samples. We validate <inline-formula><tex-math notation="LaTeX">${\rm{QFactor}}$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">${\rm{Sample}}$</tex-math></inline-formula> on a large set of circuits and discuss its hyperparameter. When incorporated in the BQSKit quantum compiler and compared against a state-of-the-art domain-specific optimizer, we demonstrate improved scalability and reduced compile time, achieving an average speedup factor of 69 for circuits with more than eight qubits. We also discuss how improved numerical optimization affects the dynamics of partitioning-based compilation schemes, which allow a tradeoff between compilation speed and solution quality.