论文标题
除了单杆易于故障量子误差校正
Beyond single-shot fault-tolerant quantum error correction
论文作者
论文摘要
为了在嘈杂的量子计算机上执行有用的计算，需要进行广泛的量子误差校正。此外，必须基于不完美的奇偶校验检查测量结果来实现量子误差校正，该测量可能会返回不正确的结果或将其他故障注入量子位。为了实现容忍性误差校正，Shor提议重复奇偶校验检查测量序列，直到观察到相同的结果很多次为止。然后，可以使用此信息执行错误校正。此容忍策略的基本实现需要$ω（r d^2）$均衡检查测量由R均衡检查定义的距离D代码。对于某些特定的高度结构化量子代码，BOMBIN表明，仅使用R测量值可以进行单次耐受性量子误差校正。在这项工作中，我们证明可以使用$ o（d \ log（d））$测量值来实现易于故障的量子误差校正。此外，我们证明了使用少于R测量值的子单个射击量允许量子误差校正方案的存在。在某些情况下，易于容忍的量子误差校正所需的奇偶校验检查测量次数成倍地小于定义代码的奇偶校验检查数量。
Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measurements until the same outcome is observed sufficiently many times. Then, one can use this information to perform error correction. A basic implementation of this fault tolerance strategy requires $Ω(r d^2)$ parity check measurements for a distance-d code defined by r parity checks. For some specific highly structured quantum codes, Bombin has shown that single-shot fault-tolerant quantum error correction is possible using only r measurements. In this work, we demonstrate that fault-tolerant quantum error correction can be achieved using $O(d \log(d))$ measurements for any code with distance $d \geq Ω(n^α)$ for some constant $α> 0$. Moreover, we prove the existence of a sub-single-shot fault-tolerant quantum error correction scheme using fewer than r measurements. In some cases, the number of parity check measurements required for fault-tolerant quantum error correction is exponentially smaller than the number of parity checks defining the code.
