D'ArQ: A QOC Framework with Causality-Aware Grouping and Basis Selection

Quantum Optimal Control (QOC) frameworks are powerful tools for compiling quantum circuits into low-latency hardware control pulses, but recent studies suffer from two critical limitations: lengthy compilation times and potential logical inconsistencies from flawed gate grouping strategies. In this work, we introduce d'ArQ, a novel QOC framework that solves these challenges. (i) We identify and resolve the causality problem, a flaw in greedy partitioning that can produce invalid schedules, by introducing a DAG-based grouping algorithm with assigning mergeability to each group so that it guarantees logical correctness. (ii) To mitigate compilation times, we use a pre-computed library of pulses derived from random unitary matrices to provide a high-quality random initialization for pulse optimization. (iii) Diverging from prior work based on GRAPE, d'ArQ is built on the GOAT algorithm. We demonstrate that the choice of analytic basis is a critical hyperparameter and introduce a heuristic cost model to dynamically select the optimal basis for each synthesis task, improving pulse performance. When evaluated against the state-of-the-art baseline PAQOC on a realistic, inhomogeneous hardware model, d'ArQ demonstrates superior performance. Notably, d'ArQ reduces circuit latency up to 22.8% and compilation time up to 56.8%, establishing a more robust and physically realistic path for circuit compilation.