Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling 3-qubit GHZ states using a rate 0.118 family of lifted product QLDPC codes and obtain a threshold of 10.7% under depolarizing noise. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of 3-qubit GHZ states to construct a scalable GHZ purification protocol.
翻译:最近构建的量子低密度平比检查(QLDPC)代码提供了逻辑正方位数和代码长度最小距离的最优化比例,从而打开通向不耐错的量子系统的大门,而资源管理管理则最少。然而,从近邻连接的表层代码到长距离互连要求的QLDPC代码的硬件路径可能是一个挑战。鉴于在根据最佳QLDPC代码建立量子系统(例如计算机)等计算机的单一结构方面的实际困难,值得考虑在相互连接的中等规模量子处理器网络上发布这种代码的分布。在这种设置中,所有综合测量和逻辑操作都必须通过使用高异端连接的表层代码来进行。由于用于净化纠结的多到1级蒸馏计划效率不高,我们在这项工作中,我们用QLDPC的量差校正校正校正校正校正校正校正校正校正值代码 QQQQ.我们用QLD 的S-deal-deal-deal-deal-deal Dal-deal-deal-deal ASal ASyal ASal ASal ASal ASal ASal ASal deal ASal ASal ASal ASal 一种我们使用了ODal ASal ASald ASal ASal ASal AS AS AS AS ASal ASal AS AS AS AS AS AS AS AS AS AS AS AS 。