A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $\mathbb{Z}_{q}\times \mathbb{Z}_{q}$ for all odd integers $q\geq 5$ and, consequently, new toric quantum codes are constructed on such square lattices regardless of whether $q$ can be represented as a sum of two squares. Furthermore this work supplies for each $q$ the polyomino shapes that tessellate the corresponding square lattices and, consequently, tile the lattice $\mathbb{Z}^{2}$. The channel without memory to be considered for these constructed toric quantum codes is symmetric, since the $\mathbb{Z}^{2}$-lattice is autodual. Moreover, we propose a quantum interleaving technique by using the constructed toric quantum codes which shows that the code rate and the coding gain of the interleaved toric quantum codes are better than the code rate and the coding gain of Kitaev's toric quantum codes for $q=2n+1$, where $n\geq 2$, and of an infinite class of Bombin and Martin-Delgado's toric quantum codes. In addition to the proposed quantum interleaving technique improves such parameters, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory.
翻译：本文展示了一种无限的量子量子组的无限量子构建程序。 通过在正方方格上为所有奇数整数$q\geq 5$, 并因此在这种平方方格上构建了新的量子代码, 不论$qq$是否代表两个方形之和。 此外, 通过为每一种参数提供一种无穷的量子结构提供一种无穷无穷的量子组式的量子代码, 将相应的正方方格成形, 从而将 lattice $\ mathb ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ }, 用于这些构建的量子量子值代码中, 没有记忆的频道是对称的, $malb2 的量子值中, 我们建议一种量间技术, 通过使用构建的量子量子值代码显示, 的量子值和内置的量子值代码的量子值的值值值的值值值值值值值值值值的值值值值值值值值值值的值值值值值值值的值值值值值值值值值值值值值值值值值比 等中, 和基基质值的量值的量值的量值的量值的量值的值值值值值值值的值值值值值的值的值值值值值值比值比值值值值值值值值值值值值值值的值值值值值值值值值值值值值值值值值比值值值的值的值值值值值值值值值值值值值值值值值值值的值的值的值的值的值的值的值的值的值的值的值的比值值的比值值值值值值值的值的值的值值值值和基值的值的值的值值的值的值的值的值的值的值的值的值值值的值的值值值值值值的值值值值值值值值值值值值值值值值值值值值值的
相关内容
微信扫码咨询专知VIP会员