General Entropic Constraints on Calderbank-Shor-Steane Codes within Magic Distillation Protocols
General Entropic Constraints on Calderbank-Shor-Steane Codes within Magic Distillation Protocols
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DOI：
10.1103/prxquantum.4.020359
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发表时间：
2022-11
期刊：
影响因子：
9.7
通讯作者：
Rhea Alexander;Si Gvirtz-Chen;Nikolaos Koukoulekidis;D. Jennings
中科院分区：
文献类型：
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作者：
Rhea Alexander;Si Gvirtz-Chen;Nikolaos Koukoulekidis;D. Jennings
魔态是容错量子计算道路上的基本基石。CSS代码在构建魔法蒸馏协议中起着至关重要的作用。以前的工作已经铸造量子计算与奇维d $$内的相空间设置，其中通用量子计算描述的quasiprobidity分布的统计力学的魔术状态。在这里，我们将这个框架扩展到重要的$d=2$量子比特的情况下，我们可以利用CSS电路中的常见结构，以获得蒸馏边界能够超越以前的单调边界的制度的实际利益。此外，在CSS代码投影的情况下，我们在CSS代码的代码长度$n$上得到了一个新的截止结果，这意味着对于固定的目标错误率和接受概率，只需要考虑CSS代码低于量子位的阈值。这些熵的限制是不是简单地由于数据处理的不平等，但依赖于这些协议的随机表示。
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.