面向任意网络拓扑分布式量子架构的Clifford电路合成
Clifford Circuit Synthesis for Distributed Quantum Architectures with Arbitrary Network Topology
AI总结：
针对任意网络拓扑的分布式量子架构，提出基于分块矩阵高斯消元的渐近最优Clifford电路合成方法，可扩展至Clifford+RZ电路，在CSS码中实现CNOT电路需O(nk)个分块间横向CNOT及分块内泡利测量。
AI中文摘要：
为实现大规模容错量子计算，将多个小型量子比特集合组合起来可能比构建单个大型集合更容易，例如通过分块码量子纠错或利用共享纠缠的分布式量子处理器。在这些场景中，整体量子计算的时间或误差预算可能由非局域操作主导，因此最小化此类操作的数量具有重要价值。我们考虑非局域和局域连接均可任意受限的情况，基于分块矩阵高斯消元法，给出分布式CNOT和Clifford电路的渐近最优合成方法。我们通过推广泡利指数电路表示，将该方法扩展到所有Clifford+RZ电路，这可自然与现有的T计数优化方法集成。作为应用，我们展示了如何在以k个分块编码n个逻辑量子比特的CSS码中实现CNOT电路，使用O(nk)个分块间横向CNOT和分块内泡利测量。
英文摘要：
To achieve large-scale fault-tolerant quantum computation, it may be easier to combine many small sets of qubits than to construct a single large set. For example via quantum error correction with block codes, or distributed quantum processors utilizing shared entanglement. In these regimes, the time or error budget of the overall quantum computation may be dominated by non-local operations. Hence, it is worthwhile to minimize the number of these operations. We consider the case where both non-local and local connectivity may be arbitrarily restricted, and give an asymptotically optimal synthesis method for distributed CNOT and Clifford circuits, based on block-matrix Gaussian elimination. We extend this to all Clifford+RZ circuits by generalizing the Pauli exponential circuit representation; this naturally integrates with existing methods for optimizing T-count. As an application, we show how to implement CNOT circuits in a CSS code encoding n logical qubits in k blocks using O(nk) inter-block transversal CNOTs and intra-block Pauli measurements.
