面向高自旋猫码的容错性：基于通用相位误差透明门
Towards fault-tolerance with universal phase-error-transparent gates for high-spin cat codes
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中文总结 AI 辅助
本研究针对高维核自旋系统，构建了对相位误差透明的通用逻辑门集合，模拟显示其性能优于非ET门，为实现全容错量子计算提供了具体路径。
中文摘要 AI 辅助
高维核自旋为量子纠错（QEC）提供了硬件高效的实现途径，其中自旋猫码对相位误差具有固有鲁棒性，而相位误差是硅基施主架构中的主导噪声通道。然而，要充分发挥该编码的潜力，需要能保留其纠错特性的门操作。本研究构建了一套对相位误差透明（ET）的通用逻辑门集合，并讨论了其实际实现方案与挑战。ET门确保门操作过程中随机发生的相位误差以系统可追踪的方式传播，且在后续QEC步骤中仍可纠正。在所构建的通用门集合中，逻辑X门是主要挑战，本文探讨了潜在实现方案。此外，为充分发挥自旋猫码相对于未编码量子比特的优势，逻辑CZ门的多频微波驱动至关重要。模拟结果显示，ET门的性能显著优于非ET门，且可能是突破盈亏平衡点的必要条件。本文进一步说明了如何通过ET操作构建逻辑测量与恢复方案，并解释了为何态制备无法实现ET。特别地，计算基下的ET测量可通过自旋宇称测量实现，且由ET操作构建的纠错电路可达到最优纠错容量。本研究为基于高维核自旋系统的全容错量子计算规划了一条具体路径。
英文摘要
High-dimensional nuclear spins offer a hardware-efficient route to quantum error correction (QEC), with the spin cat code providing intrinsic robustness against phase errors -- the dominant noise channel in donor-in-silicon architectures. However, realizing the full potential of this encoding requires gate operations that preserve its error-correcting properties. In this work, we construct a universal logical gate set that is error-transparent (ET) to phase errors, and discuss its practical implementations and challenges. The ET gates ensure that phase errors occurring stochastically during gate operations are propagated in a systematically traceable manner and remain correctable in a subsequent QEC step. Among the universal gate set constructed, we identify the logical $X$ gate as the primary challenge and discuss potential realization schemes. In addition, to fully leverage the spin cat code's advantage over an unencoded qubit, multi-tone microwave driving of the logical $CZ$ gate is essential. Our simulations show that ET gates significantly outperform non-ET gates and may be necessary to surpass the break-even point. We further show how logical measurement and recovery can be constructed from ET operations, and explain why state-preparation cannot be made ET. In particular, ET measurement in the computational basis is realizable via spin parity measurement, and that error correction circuits constructed from ET operations achieve optimal error correction capacity. Our work charts a concrete path toward full fault-tolerant quantum computation with high-dimensional nuclear spin systems.
