Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have introduced mid-circuit measurements and resets, enabling the reuse of measured qubits and significantly reducing the qubit requirements for executing quantum algorithms. In this work, we present a systematic study of dynamic quantum circuit compilation, a process that transforms static quantum circuits into their dynamic equivalents with a reduced qubit count through qubit-reuse. We establish the first general framework for optimizing the dynamic circuit compilation via graph manipulation. In particular, we completely characterize the optimal quantum circuit compilation using binary integer programming, provide efficient algorithms for determining whether a given quantum circuit can be reduced to a smaller circuit and present heuristic algorithms for devising dynamic compilation schemes in general. Furthermore, we conduct a thorough analysis of quantum circuits with practical relevance, offering optimal compilations for well-known quantum algorithms in quantum computation, ansatz circuits utilized in quantum machine learning, and measurement-based quantum computation crucial for quantum networking. We also perform a comparative analysis against state-of-the-art approaches, demonstrating the superior performance of our methods in both structured and random quantum circuits. Our framework lays a rigorous foundation for comprehending dynamic quantum circuit compilation via qubit-reuse, bridging the gap between theoretical quantum algorithms and their physical implementation on quantum computers with limited resources.

翻译：量子计算在解决复杂计算问题方面展现出巨大潜力，但其实际实现受限于计算可用量子比特的稀缺。近期量子硬件进展引入了电路中段测量与重置技术，使得已测量量子比特可重复利用，从而显著降低执行量子算法所需的量子比特数。本文系统研究了动态量子电路编译——通过量子比特重用将静态量子电路转换为等效动态电路以减少量子比特数的过程。我们首次建立了通过图操作优化动态电路编译的通用框架。具体而言，我们利用二进制整数规划完整刻画了最优量子电路编译特性，提出了判定给定量子电路能否化简为更小电路的高效算法，并给出了通用动态编译方案的启发式算法。此外，我们对具有实际意义的量子电路进行了深入分析，为量子计算中的经典量子算法、量子机器学习中使用的拟设电路及量子网络关键性的基于测量的量子计算提供了最优编译方案。我们还与现有最优方法进行了对比分析，展示了我们的方法在结构化与随机量子电路中的优越性能。该框架为理解基于量子比特重用的动态量子电路编译奠定了严格基础，弥合了理论量子算法与有限资源量子计算机物理实现之间的鸿沟。