Dual-Head Learning-Based Candidate-Gate Pruning for Efficient Quantum Unitary Synthesis

Quantum unitary synthesis (QUS) commonly employs a scalar cost-to-go predictor to guide stochastic beam search. At each search step, however, every beam element is expanded over the complete candidate-gate set before the resulting states are evaluated, yielding a -way branching factor and making candidate evaluation a major computational bottleneck. This work augments the shared network trunk with a classification head that predicts the most likely next gates from a given residual state. The predicted gate probabilities are used to prune the candidate set prior to computationally expensive per-child cost-to-go evaluation. The proposed approach includes a data-generation and pre-processing pipeline, a multilabel classification formulation, and a safety mechanism that monitors the underlying cost-to-go model and automatically restores the most recent reliable model upon performance degradation. Experiments using a trained four-qubit model demonstrate approximately 87% next-gate prediction accuracy, with improved accuracy as the prediction-set size increases. Incorporating classification-based candidate pruning reduces search time by approximately 5times. Although aggressive pruning currently results in a reduction in overall synthesis success rate under the available training data, the observed classification performance indicates that increased training data and improved prediction accuracy can enable more effective pruning and further reduce synthesis cost. All reported results and figures are obtained from actual training and evaluation runs of the accompanying implementation.