Turning gate synthesis errors into incoherent errors
Turning gate synthesis errors into incoherent errors
复制标题
将门综合错误转变为不相干错误
DOI：
10.26421/qic17.5-6-7
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Hastings
中科院分区：
文献类型：
--
作者：
M. Hastings
使用纠错码和容错技术，至少在理论上，可以产生错误率明显低于底层物理量子位的逻辑量子位。然而，假设作用于这些逻辑量子位的门只是所需门的近似。例如，在从一组Clifford和$T$门合成单个量子比特酉时，这可能会出现;对于一般的这种酉，任何有限的门序列都只能近似于所需的目标。在这种情况下，门中的误差可以相干地相加，因此，粗略地说，每个门的酉中的误差$\n $必须缩放为$\n\lesssim 1/N$，其中$N$是门的数量。然而，如果人们可以选择在期望的目标附近合成几个酉中的一个，并且如果这些选择的平均值更接近目标，我们给出了一些基本的界限，这些界限显示了可以通过对随机选择进行平均来使误差不相干地相加的情况，因此，粗略地说，人们需要$\nums\lesssim 1/\sqrt{N}$。我们评论一个特殊的应用程序，以提取魔术状态，这种效果自动发生在通常的电路。
Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on these logical qubits are only approximation of the desired gate. This can arise, for example, in synthesizing a single qubit unitary from a set of Clifford and $T$ gates; for a generic such unitary, any finite sequence of gates only approximates the desired target. In this case, errors in the gate can add coherently so that, roughly, the error $\epsilon$ in the unitary of each gate must scale as $\epsilon \lesssim 1/N$, where $N$ is the number of gates. If, however, one has the option of synthesizing one of several unitaries near the desired target, and if an average of these options is closer to the target, we give some elementary bounds showing cases in which the errors can be made to add incoherently by averaging over random choices, so that, roughly, one needs $\epsilon \lesssim 1/\sqrt{N}$. We remark on one particular application to distilling magic states where this effect happens automatically in the usual circuits.