AI 中文总结
本研究提出名为“魔法卷轴”的方法，结合偏置噪声与高量子比特连接性，改进魔法态制备，提升制备与蒸馏体积，降低错误率，适用于基于寄存器的容错量子计算架构。
AI 中文摘要
多个量子计算平台（包括中性原子[1]、氮空位中心[2,3]、门定义量子点[4-6]以及硅中的14|15磷原子量子比特[7,8]）正在实验探索超越最近邻平面晶格的高连接性量子比特。理论研究则考虑修改容错码以利用这种更高的量子比特连接性，例如非局部LDPC码[9]，这也激励了超导平台[10]和光子平台[11]寻求非平面连接性。此外，另有理论研究关注偏置噪声，即比特翻转和相位翻转错误的概率并不相等。本研究中，我们提出了利用两量子比特寄存器实现6.6.6和4.8.8颜色码，以及双层和折叠表面码的高效方法。我们还利用噪声偏置避免钩状错误，展示了与表面码相当的性能。通过结合颜色码和双层码，我们展示了如何改进魔法态制备程序[12-14]，该程序被我们称为“魔法卷轴”。魔法卷轴不仅能转换为标准表面码，还能将制备体积提升3倍，且支持低至10^-9的魔法|T⟩态保真度。我们表明，该技术可进一步用于提升蒸馏性能，在错误率约为10^-15时，蒸馏体积提升3倍。通过这些构造，我们展示了利用噪声偏置和高量子比特连接性的技术，表明基于寄存器的架构如何在容错量子计算中降低错误率并减少量子体积。
英文摘要
Multiple quantum computing platforms across neutral atoms [1], nitrogen vacancy centres [2, 3], gate-defined dots [4-6] and 14|15 phosphorus atom qubits [7, 8] in silicon are experimentally exploring the use of high connectivity qubits, beyond that of nearest-neighbour planar lattices. Theoretical works consider modifications to fault-tolerant codes to leverage this higher qubit connectivity, such as non-local LDPC codes [9], inspiring superconducting [10] and photonic [11] platforms to also seek non-planar connectivity. In addition, separate theoretical works consider biased noise, where bit- and phase-flip errors are not equally likely. In this work, we present efficient methods for implementing 6.6.6 and 4.8.8 colour codes, as well as bilayer and folded surface codes, using two-qubit registers. We also leverage noise bias to avoid hook errors, demonstrating comparable performance to the surface code. By combining colour and bilayer codes, we show how magic state cultivation procedures [12-14] can be improved, in a procedure we refer to as the Magic Scroll. Not only does the Magic Scroll escape to a standard surface code, it also improves cultivation volumes by 3x and supports magic $|T\rangle$ state fidelities as low as $10^{-9}$. We show that this technique can be further leveraged to improve distillation performance, showing a 3x improvement to distillation volumes for error rates of $\sim 10^{-15}$. Through these constructions, we demonstrate techniques to leverage noise bias and high qubit connectivity, showing how register-based architectures can improve error rates and reduce quantum volumes in fault-tolerant quantum computing.
CommentsMain text: 22 pages, 10 figures, 2 tables. Supplementary: 24 pages, 24 figures, 1 table
