Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the number of such expensive gates could mean the difference between being able to run a circuit or not. While exact synthesis is exponentially hard in the number of qubits, local synthesis approaches are commonly used to compile large circuits by decomposing them into substructures. However, composing local methods leads to suboptimal compilations in key metrics such as $T$-count or circuit depth, and their performance strongly depends on circuit representation. In this work, we address this challenge by proposing \textsc{Q-PreSyn}, a strategy that, given a set of local edits preserving circuit equivalence, uses a RL agent to identify effective sequences of such actions and thereby obtain circuit representations that yield a reduced $T$-count upon synthesis. Experimental results of our proposed strategy, applied on top of well-known synthesis algorithms, show up to a $20\%$ reduction in $T$-count on circuits with up to 25 qubits, without introducing any additional approximation error prior to synthesis.

翻译：将量子电路编译为Clifford+$T$门集合是利用稳定子码实现容错量子计算的核心任务。在近期发展中，$T$门将成为容错实现成本的主要因素，减少此类昂贵门的数量可能直接决定电路能否实际运行。虽然精确合成在量子比特数量上具有指数级复杂度，但局部合成方法通常通过将大型电路分解为子结构进行编译。然而，局部方法的组合会导致在$T$门数量或电路深度等关键指标上产生次优编译结果，且其性能高度依赖于电路表示形式。本研究通过提出\textsc{Q-PreSyn}策略应对这一挑战：该策略在给定保持电路等价性的局部编辑操作集合的前提下，利用强化学习智能体识别有效的操作序列，从而获得能在合成后降低$T$门数量的电路表示形式。将我们提出的策略应用于经典合成算法的实验结果表明，在不超过25个量子比特的电路上可实现高达$20\%$的$T$门数量缩减，且不会在合成前引入任何额外近似误差。