论文标题
量子错误源和通道编码
Quantum Error Source and Channel Coding
论文作者
论文摘要
介绍了一块逻辑Qubits的经典编码。我们在与经典错误校正代码的双重代码相对应的逻辑Qubits上表征了产品稳定器组的子组。我们证明了一组可更正误差模式的条件，允许根据查找表进行明确的解码。对于大型古典代数代码的大家庭，我们表明综合征从$ l $逻辑量子尺度提取综合征所需的量子开销为$ {\ cal o}（\ cal o}（\ log_2（l+1）），$渐变。基本构造适用于考虑双重和测量错误，同时仍采用基于查找表的解码器。此外，我们表征了一组可检测的误差，并展示了古典代数解码器即使在存在综合征噪声的情况下，也可以明确地定位逻辑量子器。我们认为，从香农意义上讲，量子误差校正更恰当地将其视为源压缩，而香农的源和通道编码定理在编码量子寄存器的水平上为量子误差校正任务的高架速率（例如量子误差校正）提供了界限。
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on the set of correctable error patterns allowing for unambiguous decoding based on a lookup table. For a large family of classical algebraic codes, we show that the qubit overhead required for syndrome extraction from $L$ logical qubits scales as ${\cal O}(\log_2(L+1)),$ asymptotically. The basic construction is adapted to account for two-qubit and measurement errors, while still employing a lookup table based decoder. Moreover, we characterize the set of detectable errors and show how classical algebraic decoders can unambiguously locate logical qubits with errors even in the presence of syndrome noise. We argue that quantum error correction is more aptly viewed as source compression in the sense of Shannon, and that Shannon's source and channel coding theorems provide bounds on the overhead rates of quantum post-selection tasks, such as quantum error correction, at the level of the encoded quantum register.
