Structured near-optimal channel-adapted quantum error correction
Structured near-optimal channel-adapted quantum error correction
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DOI：
10.1103/physreva.77.012320
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发表时间：
2008-01-01
影响因子：
2.9
通讯作者：
Win, Moe Z.
中科院分区：
文献类型：
--
作者：
Fletcher, Andrew S.;Shor, Peter W.;Win, Moe Z.
我们提出了一类数值算法，将量子纠错方案应用于信道模型。给定编码和通道模型，先前表明最大化平均纠缠保真度的量子操作可以通过半定程序（SDP）计算，这是一种凸优化。虽然是最佳的，但是对于长代码来说，这种恢复操作在计算上是困难的。此外，最优恢复操作没有超出完全正跟踪保留约束的结构。我们推导出生成结构化通道适应错误恢复操作的方法。具体来说，每个恢复操作都以投影错误综合症测量开始。计算结构化恢复操作的算法比 SDP 更具可扩展性，并且具有直观的物理形式的产量恢复操作。使用拉格朗日对偶性，我们得出性能界限以证明接近最优。
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace-preserving constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality.