Optimal wire cutting with classical communication

TL;DR

The paper addresses the challenge of executing large quantum circuits on devices with few qubits by circuit knitting, focusing on wire cuts and gate cuts under a unifying quasiprobability framework. It derives the exact optimal sampling overhead for wire cuts in two regimes: without classical communication, the overhead scales as $O(16^n)$, while with classical communication it scales as $O(4^n)$, and extends these results to arbitrary cut positions. A teleportation-based protocol shows that the overhead with classical communication is strictly submultiplicative and allows cutting multiple wires in parallel or at arbitrary positions, with explicit bounds $\gamma_{LOCC}=2^{n+1}-1$ and corresponding sampling overhead $(2^{n+1}-1)^2$. These findings provide tight, general optima for wire-cutting costs within the quasiprobability paradigm, clarifying when CC yields meaningful improvements and how to balance ancilla resources. The work has practical implications for near-term quantum computing and modular quantum architectures, enabling more efficient partitioning strategies for large circuits.

Abstract

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.

Figures (5)

• Figure 1: Two example circuits demonstrating the differences between wire and gate cuts.
• Figure 2: Two examples explaining the settings \ref{['it_b']} and \ref{['it_c']}.
• Figure 3: The task of wire cutting can be translated into the framework of quasiprobabilistic gate cutting. This figure is explained in the main text.
• Figure 4: Circuit performing a teleportation of the state $\ket{\psi}$ using an ebit $\ket{\Psi}$ and LOCC.
• Figure 5: Sampling overhead per wire cut for different scenarios. The x-axis denotes the number of wire cuts.

Theorems & Definitions (14)

• Lemma 2.1: PS22
• Lemma 2.2: PS22
• Lemma 3.1
• proof
• Lemma 3.2
• proof
• Proposition 3.3
• proof
• Proposition 4.1
• proof