利用非稳定子态容错实现密集旋转操作

Fault-tolerantly implementing dense rotation operations based on non-stabilizer states

Non-Clifford操作不能在量子纠错码上自然横向实现,但可通过辅助量子态和在量子纠错码上能横向实现的Clifford操作来容错实现,从而取得容错量子计算的通用性.非平庸的单量子比特操作是Non-Clifford操作,可以分解为绕z轴和绕x轴非平庸旋转操作的组合.本文首先介绍了利用非稳定子态容错实现绕z轴和绕x轴旋转的操作,进而设计线路利用魔幻态容错制备非稳定子态集,最后讨论了运用制备的非稳定子态集模拟任意非平庸单量子比特操作的问题.与之前工作相比,制备非稳定子态的线路得到简化,成功概率提高,且在高精度模拟任意单量子比特操作时所消耗的非稳定子态数目减少了50%.

Based on the quantum error-correction codes and concatenation, quantum logical gates can be implemented transversally, which is called the fault-tolerant quantum computation. Clifford gates can be directly and fault-tolerantly performed, but they cannot reach universal quantum computation. How to implement the non-Clifford gate fault-tolerantly is a vital technique in fault-tolerant universal quantum computation. Here the magic state is selected to help the implementing of the non-Clifford gate transversally. Based on the non-stabilizer state cosθi｜0？＋sinθi｜1？, circuits which can execute 2θi rotation around X-axis and Z-axis fault-tolerantly are proposed. Then new non-stabilizer states in this form are developed and produced from the distilled magic state. By using these states, a number of non-Clifford gates can be performed transversally, which makes profound implication in fault-tolerant quantum computation. We calculate the number of the non-stabilizer states needed for simulating the desired rotation operations, which is less than that in previous protocols.