论文标题
通过有限参考框架校正最佳通用量子误差
Optimal Universal Quantum Error Correction via Bounded Reference Frames
论文作者
论文摘要
使用一组通用横向门的错误校正代码是量子计算的逃避代码。但是，这种代码被Eastin-Knill定理排除在外。此外，该定理还排除了相互协变的代码，这些代码相对于形成连续对称性的横向单一操作的作用。在这项工作中，从任意代码开始，我们使用量子参考框架构建了相对于整个尺寸$ d $的本地统一门的协变量的近似代码。我们表明，我们的代码能够有效纠正不同类型的擦除错误。当删除构建代码的$ n $ qudits的一小部分时，我们的协变量代码的错误将缩放为$ 1/n^2 $，这让人联想到量子计量的海森伯格限制。当每个Qudit都有被删除的机会时，我们的协变量代码的错误将缩放为$ 1/n $。我们表明，在两种情况下，误差缩放量都是最佳的。我们的方法对容忍量子计算，参考框架误差校正和ADS-CFT二元性具有影响。
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate codes which are covariant with respect to the entire group of local unitary gates in dimension $d$, using quantum reference frames. We show that our codes are capable of efficiently correcting different types of erasure errors. When only a small fraction of the $n$ qudits upon which the code is built are erased, our covariant code has an error that scales as $1/n^2$, which is reminiscent of the Heisenberg limit of quantum metrology. When every qudit has a chance of being erased, our covariant code has an error that scales as $1/n$. We show that the error scaling is optimal in both cases. Our approach has implications for fault-tolerant quantum computing, reference frame error correction, and the AdS-CFT duality.
