Leakage mitigation for quantum error correction using a mixed qubit scheme
Leakage mitigation for quantum error correction using a mixed qubit scheme
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DOI：
10.1103/physreva.100.032325
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发表时间：
2019-04
影响因子：
2.9
通讯作者：
N. C. Brown;K. Brown
中科院分区：
文献类型：
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作者：
N. C. Brown;K. Brown
泄漏错误将量子比特从计算子空间中取出，如果不解决，则会累积。泄漏的量子比特将降低量子纠错协议的有效性，这是由于实现泄漏减少电路的成本以及泄漏状态与量子比特状态相互作用所造成的危害。由拉曼门驱动的离子阱量子比特在以可能泄漏的磁不敏感超精细状态编码的量子比特和以不能泄漏的电子自旋的磁敏感塞曼状态编码的量子比特之间具有自然选择。在我们以前的工作中，我们比较了这两个量子比特的情况下的复曲面代码与去极化泄漏误差模型，并发现，对于磁场噪声的标准偏差小于32 $\mu$G，$^{174}$Yb$^+$塞曼量子比特优于$^{171}$Yb$^+$超精细量子比特。在这里，我们研究了一个物理动机的泄漏误差模型的基础上，通过Molmer-Sorenson门离子相互作用。我们发现，这大大提高了超精细量子比特的性能，但塞曼量子比特更有效的磁场噪声的标准偏差小于10 $\mu$G。在这些低磁场下，我们发现最好的选择是混合量子位方案，其中超精细量子位是辅助，并且在不需要额外的泄漏减少电路的情况下处理泄漏。
Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic field noise with a standard deviation less than 32 $\mu$G that the $^{174}$Yb$^+$ Zeeman qubit outperforms the $^{171}$Yb$^+$ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the Molmer-Sorenson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic field noise with a standard deviation less than 10 $\mu$G. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the ancilla and the leakage is handled without the need of an additional leakage reduction circuit.