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arXiv:2603.26278

Decomposition of Multi-Qubit Gates for Circuit Cutting

Ryota Tamura, Tomoya Kashimata, Yohei Hamakawa, Kosuke Tatsumura, Hiroshi Imai

quant-phcs.ETSubmitted Mar 27, 2026• Announced Mar 30, 2026• 0 citations
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Abstract

A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical post-processing from their measurement (sampling) results. In this process, appropriate cut locations are identified after the user-designed quantum circuit, including multi-qubit gates that act on three or more qubits, has been decomposed into single-qubit gates and two-qubit gates such as the CNOT gate. Here, we present a method for reducing the sampling overhead, which refers to the increase in the number of samples required due to the cutting process, by modifying the decomposition strategy of multi-qubit gates. Using MCX and CCCX gates as representatives of multi-qubit gates, we demonstrate that the proposed decomposition method, which introduces a small number of ancilla qubits according to the identified cut locations, effectively decreases the sampling overhead.

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8 pages, 7 figures, 1 table

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A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical post-processing from their measurement (sampling) results. In this process, appropriate cut locations are identified after the user-designed quantum circuit, including multi-qubit gates that act on three or more qubits, has been decomposed into single-qubit gates and two-qubit gates such as the CNOT gate. Here, we present a method for reducing the sampling overhead, which refers to the increase in the number of samples required due to the cutting process, by modifying the decomposition strategy of multi-qubit gates. Using MCX and CCCX gates as representatives of multi-qubit gates, we demonstrate that the proposed decomposition method, which introduces a small number of ancilla qubits according to the identified cut locations, effectively decreases the sampling overhead.
Circuit cutting, the decomposition of a quantum circuit into independent partitions, has become a promising avenue towards experiments with larger quantum circuits in the noisy-intermediate scale quantum (NISQ) era. While previous work focused on cutting qubit wires or two-qubit gates, in this work we introduce a method for cutting multi-controlled Z gates. We construct a decomposition and prove the upper bound O(62K) on the associated sampling overhead, where K is the number of cuts in the circuit. This bound is independent of the number of control qubits but can be further reduced to O(4.52K) for the special case of CCZ gates. Furthermore, we evaluate our proposal on IBM hardware and experimentally show noise resilience due to the strong reduction of CNOT gates in the cut circuits.
Quantum circuit cutting enables the execution of large circuits on devices with a limited number of qubits by partitioning circuits into independent subcircuits. However, this introduces a sampling overhead, which grows exponentially with the number of cuts, rendering the choice of cut placements critical for practical circuit cutting. Determining optimal cut placements remains computationally challenging, particularly as circuits grow in size. Additionally, existing circuit cutting approaches typically treat gate and wire cuts independently. Those combining both cutting approaches, however, do not take advantage of joint cutting, i.e., identifying common gate groups and cutting them jointly for a reduced overhead. This work presents a unified framework that combines gate and wire cutting within a single partitioning strategy, enabling more efficient circuit decompositions. Moreover, our approach incorporates joint cutting via a novel gate grouping technique, further reducing sampling overhead. By formulating the cut placement problem as a scalable graph partitioning task, our method efficiently identifies near-optimal cut placements for large circuits, also providing diagnostic feedback on whether circuits are suitable for cutting.
A restriction in the quality and quantity of available qubits presents a substantial obstacle to the application of near-term and early fault-tolerant quantum computers in practical tasks. To confront this challenge, some techniques for effectively augmenting the system size through classical processing have been proposed; one promising approach is quantum circuit cutting. The main idea of quantum circuit cutting is to decompose an original circuit into smaller subcircuits and combine outputs from these subcircuits to recover the original output. Although this approach enables us to simulate larger quantum circuits beyond physically available circuits, it needs classical overheads quantified by two metrics: the sampling overhead in the number of measurements to reconstruct the original output, and the number of channels in the decomposition. Thus, it is crucial to devise a decomposition method that minimizes both of these metrics, thereby reducing the overall execution time. This paper studies the problem of decomposing the n -qubit identity channel, i.e., n -parallel wire cutting, into a set of local operations and classical communication; then we give an optimal wire-cutting method composed of channels based on mutually unbiased bases that achieves minimal overheads in both the sampling overhead and the number of channels, without ancilla qubits. This is in stark contrast to the existing method that achieves the optimal sampling overhead yet with ancilla qubits. Moreover, we derive a tight lower bound on the number of channels in parallel wire cutting without ancilla systems and show that only our method achieves this lower bound among the existing methods. Notably, our method shows an exponential improvement in the number of channels, compared to the aforementioned ancilla-assisted method that achieves optimal sampling overhead. Our work significantly alleviates the additional overheads for the wire-cutting method and may provide essential components for the early success of quantum computing. Published by the American Physical Society 2024
Quasiprobabilistic cutting techniques allow us to partition large quantum circuits into smaller subcircuits by replacing non-local gates with probabilistic mixtures of local gates. The cost of this method is a sampling overhead that scales exponentially in the number of cuts. It is crucial to determine the minimal cost for gate cutting and to understand whether allowing for classical communication between subcircuits can improve the sampling overhead. In this work, we derive a closed formula for the optimal sampling overhead for cutting an arbitrary number of two-qubit unitaries and provide the corresponding decomposition. We find that cutting several arbitrary two-qubit unitaries together is cheaper than cutting them individually and classical communication does not give any advantage.
Circuit cutting, the partitioning of quantum circuits into smaller independent fragments, has become a promising avenue for scaling up current quantum-computing experiments. Here, we introduce a scheme for joint cutting of two-qubit rotation gates based on a virtual gate-teleportation protocol. With that, we significantly lower the previous upper bounds on the sampling overhead and prove the optimality of the scheme. Furthermore, we show that no classical communication between the circuit partitions is required. For parallel two-qubit rotation gates we derive an optimal ancilla-free decomposition, which includes cnot gates as a special case.
Circuit cutting is a technique for simulating large quantum circuits by partitioning them into smaller subcircuits, which can be executed on smaller quantum devices. The results from these subcircuits are then combined in classical postprocessing to accurately reconstruct the expectation value of the original circuit. Circuit cutting introduces a sampling overhead that grows exponentially with the number of gates and qubit wires that are cut. Many recently developed quasiprobabilistic circuit cutting techniques leverage classical side information, obtained from intermediate measurements within the subcircuits, to enhance the postprocessing step. In this work, we provide a formalization of general circuit cutting techniques utilizing side information through quantum instruments. With this framework, we analyze the advantage that classical side information provides in reducing the sampling overhead of circuit cutting. Surprisingly, we find that in certain scenarios, side information does not yield any reduction in sampling overhead, whereas in others it is essential for circuit cutting to be feasible at all. Furthermore, we present a lower bound for the optimal sampling overhead with side information that can be evaluated efficiently via semidefinite programming and improves on all previously known lower bounds.