Łodyga Justyna, Mazurek Paweł, Grudka Andrzej, Horodecki Michał
Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.
1] Institute for Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland [2] National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
Sci Rep. 2015 Mar 10;5:8975. doi: 10.1038/srep08975.
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for two other codes. We show that the fidelity of the protected qubit in the noisy scenario in a large code size limit is of , where p is a probability of error on a single qubit per time step. Regarding Haah code we provide noiseless scheme, leaving the noisy case as an open problem.
我们提出了一种基于综合征测量对CSS码的未知状态进行编码和解码的方案。我们通过基塔耶夫环面码、缺陷晶格码、拓扑子系统码和3D哈阿码来说明我们的方法。只要在给定的码中逻辑算子之间的交叉由最近邻对组成，该协议就是局部的，上述码均满足这一点。对于子系统码，我们还提出了在有噪声情况下的方案，其中我们允许量子比特上的比特翻转和相位翻转错误以及状态制备和综合征测量错误。可以为其他两种码构建类似的方案。我们表明，在大码尺寸极限下的噪声场景中，受保护量子比特的保真度为 ，其中p是每个时间步长单个量子比特上的错误概率。关于哈阿码，我们提供了无噪声方案，将有噪声情况留作一个开放问题。
