A Precision and Efficiency Advantage in Continuous-Variable Quantum Compiler for Optical Phase Variational Learning

The primary objective of quantum compilation is to learn a specific quantum unitary transformation by refining an adjustable quantum circuit. This refinement is crucial for designing size- and depth-efficient quantum circuits and can potentially serve as a tool for characterizing the behavior of quantum materials. Recent work has predominantly been directed toward compilation for discrete-variable systems, while continuous-variable platforms have received less attention. However, the theory for continuous-variable quantum compilation promises to reduce the training data needed for compilation, enhance the precision of parameter estimation compared to a discrete-variable quantum compiler or classical methods and surmount the challenges of energy-dependent barren plateaus. In this context, our investigation introduces a continuous-variable variational quantum compiler tailored for learning optical quantum circuits. This compiler is adept at efficiently and precisely learning Gaussian unitary operations. As proof of principle, we experimentally demonstrate the training of a parameterized linear phase unitary to approximate a parameterized target phase unitary. The results reveal a sixfold enhancement in phase estimation precision and a twenty-two-fold reduction in time-to-solution when employing quantum entanglement, in addition to evidence of the avoidance of energy-dependent barren plateaus in noisy intermediate-scale continuous-variable variational quantum algorithms.