When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very different for compiled unitaries, which arise from programming and typically have short circuits, as compared with generic unitaries, which use all parameters and typically require circuits of maximal size. We show that simple gradient descent reliably finds depth- and gate-optimal circuits for generic unitaries, including in the presence of restricted chip connectivity. This runs counter to earlier evidence that optimal synthesis required combinatorial search, and we show that this discrepancy can be explained by avoiding the random selection of certain parameter-deficient circuit skeletons.

翻译：当门集合包含连续参数时，使用精确方法总能将酉算子合成为量子电路，但高效寻找最小电路仍是一个具有挑战性的问题。对于编译产生的酉算子（通常具有短电路）与通用酉算子（使用全部参数且通常需要最大规模电路）而言，其优化图景存在显著差异。我们证明，简单梯度下降法能够可靠地为通用酉算子找到深度最优与门最优的电路，即使在受限芯片连接性的条件下亦然。这一结论与早期认为最优合成需要组合搜索的证据相悖，我们通过避免随机选择某些参数缺失的电路骨架来解释这种差异。