We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade--offs between the number of physical qubits and the fault-tolerant execution time of a quantum algorithm. We consider a concept architecture comprising a dedicated zone as a multi-level magic state factory and a core processor for efficient logical operations, forming a supply chain network for production and consumption of magic states. Using a heuristic algorithm, we solve the multi-objective optimization problem of minimizing space and time subject to a user-defined error budget for the success of the computation, taking the performance of various fault-tolerant protocols such as quantum memory, state preparation, magic state distillation, code growth, and logical operations into account. As an application, we show that physical quantum resource estimation reduces to a simple model involving a small number of key parameters, namely, the circuit volume, the error prefactors ($\mu$) and error suppression rates ($\Lambda$) of the fault-tolerant protocols, and an allowed slowdown factor ($\beta$). We show that, in the proposed architecture, $10^5$--$10^8$ physical qubits are required for quantum algorithms with $T$-counts in the range $10^6$--$10^{15}$ and logical qubit counts in the range $10^2$--$10^4$, when run on quantum computers with quantum memory $\Lambda$ in the range 3--10, for all slowdown factors $\beta \geq 0.2$.

翻译：本文提出一种优化模块化容错量子计算架构的新方法，该方法充分考虑了量子算法物理量子比特数量与容错执行时间之间任意期望的时空权衡。我们研究的概念架构包含一个作为多层级魔法态工厂的专用区域，以及一个用于高效逻辑操作的核心处理器，二者构成了魔法态生产与消耗的供应链网络。通过启发式算法，我们在满足用户定义的计算成功误差预算前提下，求解了最小化空间与时间的多目标优化问题，并综合考虑了量子存储、态制备、魔法态提纯、码增长及逻辑操作等多种容错协议的性能。作为应用，我们展示了物理量子资源估算可简化为一个仅涉及少量关键参数的简单模型，这些参数包括：电路体积、容错协议的误差前置因子($\mu$)与误差抑制率($\Lambda$)，以及允许的减速因子($\beta$)。研究表明，在所提出的架构中，对于$T$门数量在$10^6$--$10^{15}$范围内、逻辑量子比特数在$10^2$--$10^4$范围内的量子算法，当运行在量子存储$\Lambda$值为3--10的量子计算机上时，在所有减速因子$\beta \geq 0.2$的条件下，需要$10^5$--$10^8$个物理量子比特。