Space and Time Cost of Continuous Rotations in Surface Codes
中文速览 本文深入研究了在表面码架构下实现连续旋转门的实际时空成本。传统观点认为，减少T门数量是优化容错量子算法的关键。然而，本文指出，随着魔术态蒸馏技术的进步，总运行时间或物理量子比特数（即时空体积）是更根本的成本指标。文章的核心贡献在于，它首次为一种名为“催化剂塔”的高级旋转合成技术构建了明确的表面码物理布局，并与传统的Clifford+T门合成方法进行了全面的资源成本比较。研究以期权定价算法中的两个实用子程序为例，进行了详细分析。主要结论是：在低到中等码距（这正是早期容错量子计算机的典型工作范围）下，催化剂塔不仅能显著缩短运行时间，还能降低总体的时空体积，表现出比传统方法更高的效率。然而，在高码距下，催化剂塔引入的额外辅助量子比特开销会超过其节省的T门成本，此时传统门合成方法反而更优。 因此，该研究为早期容错应用中的算法选择和硬件资源评估提供了重要的量化依据。 English Research Briefing Research Briefing: Space and Time Cost of Continuous Rotations in Surface Codes 1. The Core Contribution This paper provides a holistic, architecture-aware resource analysis of implementing continuous-angle rotation gates on a surface code quantum computer. The central thesis is that the optimal implementation strategy is not universal but depends critically on the operating regime, specifically the code distance \(d\). The authors conclude that “catalyst tower” circuits—an advanced technique for parallelizing rotations—are superior to conventional Clifford+T gate synthesis at the low-to-medium code distances expected for early fault-tolerant devices, offering reductions in both runtime and overall spacetime volume. However, at high code distances, the substantial ancilla qubit overhead required by catalyst towers makes conventional synthesis the more resource-efficient approach. This work reframes the optimization problem from minimizing abstract T-counts to minimizing concrete spacetime cost on a realistic hardware platform. ...