利用经典通信实现最优线路切割
Optimal wire cutting with classical communication
AI总结：
本文研究量子线路编织中的线路切割问题，证明子线路间无经典通信和有经典通信时切割 n 条线路的最优代价分别为 O(16^n) 与 O(4^n)。
摘要：
线路编织（circuit knitting）是将大型量子线路划分为较小子线路的过程，使得只需运行这些子线路即可推断出原线路的结果。由于有限的量子比特数量很可能成为展示量子优势的主要瓶颈，此类技术对于近期和早期容错量子计算机至关重要。在划分线路时，人们通常会区分门切割和线路切割。任何线路编织方法的代价都随切割数量呈指数级增长。实现切割的一种可能方式是通过准概率模拟技术。事实上，我们认为所有现有的严格线路编织技术都可以在这一框架下理解。此外，我们刻画了在子线路可以或不可以交换经典信息情况下线路切割的最优开销。我们证明，在子线路之间没有经典通信和有经典通信的情况下，切割 n 条线路的最优代价分别按 O(16^n) 和 O(4^n) 缩放。
英文摘要：
Circuit knitting is the process of partitioning large quantum circuits into smaller subcircuits such that the result of the original circuits can be deduced by only running the subcircuits. Such techniques will be crucial for near-term and early fault-tolerant quantum computers, as the limited number of qubits is likely to be a major bottleneck for demonstrating quantum advantage. One typically distinguishes between gate cuts and wire cuts when partitioning a circuit. The cost for any circuit knitting approach scales exponentially in the number of cuts. One possibility to realize a cut is via the quasiprobability simulation technique. In fact, we argue that all existing rigorous circuit knitting techniques can be understood in this framework. Furthermore, we characterize the optimal overhead for wire cuts where the subcircuits can exchange classical information or not. We show that the optimal cost for cutting $n$ wires without and with classical communication between the subcircuits scales as $O(16^n)$ and $O(4^n)$, respectively.
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