论文标题
使用张量 - 网络解码器，用于针对Pauli噪声的量子编码的低深度随机电路
Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder
论文作者
论文摘要
最近的工作[M. J. Gullans等人，物理审查X，11（3）：031066（2021）]表明，由随机Clifford编码循环定义的量子误差纠正代码可以在校正错误时达到非编码率，即使在$ N $ QUBIT上的随机电路，嵌入了一个空间上的空间凹陷（1D），也可以达到$ N $ QUBITS（1D）的$ N $ QUBITS（1D）。 $ d = \ MATHCAL {O}（\ log {n}）$。但是，仅对简单的擦除噪声模型证明了这一点。在这项工作中，我们发现这种所需的财产确实适用于传统的Pauli噪声模型。具体而言，我们从数值上证明，即使在电路深度仅限于$ d = $ d = \ Mathcal {o}（O}（O}（\ log n）$中，即使在1D中，也可以达到各种优势，即使在电路深度限制到$ d = $ d = $ d = $ d = $ d = $ d = $ d = $ d时，也可以达到$ d = \ mathcal {o}（n）$ - 深度随机编码电路的限制，即通过开发张量 - 网络最大样本解码算法，该算法有效地适用于$ \ log $ -Deppth编码1D中的电路。
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the random circuits on $n$ qubits, embedded in one spatial dimension (1D), have a logarithmic depth $d=\mathcal{O}(\log{n})$. However, this was demonstrated only for a simple erasure noise model. In this work, we discover that this desired property indeed holds for the conventional Pauli noise model. Specifically, we numerically demonstrate that the hashing bound, i.e., a rate known to be achieved with $d=\mathcal{O}(n)$-depth random encoding circuits, can be attained even when the circuit depth is restricted to $d=\mathcal{O}(\log n)$ in 1D for depolarizing noise of various strengths. This analysis is made possible with our development of a tensor-network maximum-likelihood decoding algorithm that works efficiently for $\log$-depth encoding circuits in 1D.
