论文标题
魔术蒸馏协议中CSS代码的一般熵约束
General entropic constraints on CSS codes within magic distillation protocols
论文作者
论文摘要
魔术状态是通往耐故障量子计算的道路上的基本构件。 CSS代码在魔术蒸馏协议的构建中起着至关重要的作用。先前的工作在奇数尺寸$ d $的魔术状态下施放了量子计算，在一个相空间设置中，通用量子计算由验分布的统计力学描述。在这里，我们将此框架扩展到重要的$ d = 2 $ QUBIT案例，并表明我们可以利用CSS电路中的共同结构，以获得能够超过实际利益制度的先前单调界限的蒸馏界。此外，在CSS代码预测的情况下，我们在表征所需蒸馏的参数方面对CSS代码的代码长度$ n $产生了新的截止结果，这意味着对于固定的目标错误率和接受概率，一个人只需要考虑CSS代码低于threshold qubits的CSS代码。这些熵约束并不仅仅是由于数据处理不等式而明确依赖于此类协议的随机表示。
Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. CSS codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for odd dimension $d$ within a phase space setting in which universal quantum computing is described by the statistical mechanics of quasiprobability distributions. Here we extend this framework to the important $d=2$ qubit case and show that we can exploit common structures in CSS circuits to obtain distillation bounds capable of out-performing previous monotone bounds in regimes of practical interest. Moreover, in the case of CSS code projections, we arrive at a novel cut-off result on the code length $n$ of the CSS code in terms of parameters characterising a desired distillation, which implies that for fixed target error rate and acceptance probability, one needs only consider CSS codes below a threshold number of qubits. These entropic constraints are not due simply to the data-processing inequality but rely explicitly on the stochastic representation of such protocols.
