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New Journal of Physics

A generalized reconstruction model in circuit cutting and nonlocal-gate-based distributed quantum computation

Yi Sun, Changhua Zhu, Yuan Zhao, Guangwu Hou

Published Oct 28, 2025• 0 citations
Publisher

Abstract

Abstract In the current noisy intermediate-scale quantum era, the limited number of high-fidelity qubits and restricted circuit depth pose significant challenges for large-scale quantum computation. Fortunately, distributed quantum computing (DQC) provides a feasible solution by dividing large quantum circuits into smaller subcircuits that can be executed on existing quantum processors. In this work, we propose a generalized model of circuit reconstruction (GMCR), which is capable of handling complex cutting patterns such as U-type structures to recover the output of the original circuit from the subcircuit results. In addition to the number of nonlocal gates and execution rounds, we introduce a new objective function in multi-objective simulated annealing (MOSA)-based cutting algorithm, the number of required SWAP operations in the subsequent mapping from logical qubits to physical qubits, which is used to satisfy the hardware connectivity constraints and to further decrease the complexity of quantum circuit compiling. We verified the GMCR model by cutting five circuits: encoding circuit for the Steane 7-qubit code, circuit of Shor’s algorithm, quantum supremacy circuit, quantum circuit of Bernstein–Vazirani algorithm, and circuit of approximate quantum Fourier transform. In the case of the Steane 7-qubit code, the number of reconstruction rounds was reduced from 337 to 156 under a fixed nonlocal gate count of two, while the number of SWAP operations was also reduced from 10 to 7 compared with the earlier MOSA-based algorithm. For the U-type subcircuits, using the GMCR model, the original results can be obtained, but cannot be obtained by the dynamic definition, approximate reconstruction algorithm, and fast reconstruction algorithm. This work plays an important role in implementing large-scale DQC, a typical application of future quantum Internet.

DOI
10.1088/1367-2630/ae1866

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Abstract In the current noisy intermediate-scale quantum era, the limited number of high-fidelity qubits and restricted circuit depth pose significant challenges for large-scale quantum computation. Fortunately, distributed quantum computing (DQC) provides a feasible solution by dividing large quantum circuits into smaller subcircuits that can be executed on existing quantum processors. In this work, we propose a generalized model of circuit reconstruction (GMCR), which is capable of handling complex cutting patterns such as U-type structures to recover the output of the original circuit from the subcircuit results. In addition to the number of nonlocal gates and execution rounds, we introduce a new objective function in multi-objective simulated annealing (MOSA)-based cutting algorithm, the number of required SWAP operations in the subsequent mapping from logical qubits to physical qubits, which is used to satisfy the hardware connectivity constraints and to further decrease the complexity of quantum circuit compiling. We verified the GMCR model by cutting five circuits: encoding circuit for the Steane 7-qubit code, circuit of Shor’s algorithm, quantum supremacy circuit, quantum circuit of Bernstein–Vazirani algorithm, and circuit of approximate quantum Fourier transform. In the case of the Steane 7-qubit code, the number of reconstruction rounds was reduced from 337 to 156 under a fixed nonlocal gate count of two, while the number of SWAP operations was also reduced from 10 to 7 compared with the earlier MOSA-based algorithm. For the U-type subcircuits, using the GMCR model, the original results can be obtained, but cannot be obtained by the dynamic definition, approximate reconstruction algorithm, and fast reconstruction algorithm. This work plays an important role in implementing large-scale DQC, a typical application of future quantum Internet.
Abstract In the current noisy intermediate-scale quantum (NISQ) era, the number of qubits and the depth of quantum circuits in a quantum computer are limited because of complex operation among increasing number of qubits, low-fidelity quantum gates under noise, and short coherence time of physical qubits. However, with distributed quantum computation (DQC) in which multiple small-scale quantum computers cooperate, large-scale quantum circuits can be implemented. In DQC, it is a key step to decompose large-scale quantum circuits into several small-scale subcircuits equivalently. In this paper, we propose a quantum circuit cutting scheme for the circuits consisting of only single-qubit gates and two-qubit gates. In the scheme, the number of non-local gates and the rounds of subcircuits operation are minimized by using the multi-objective simulated annealing (MOSA) algorithm to cluster the gates and to choose the cutting positions whilst using non-local gates. A reconstruction process is also proposed to calculate the probability distribution of output states of the original circuit. As an example, the 7-qubit circuit of Shor algorithm factoring 15 is used to verify the algorithm. Five cutting schemes are recommended, which can be selected according to practical requirements. Compared with the results of the mixing integer programming (MIP) algorithm, the number of execution rounds is efficiently reduced by slightly increasing the number of nonlocal gates.
Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.
Executing large quantum circuits is not feasible using the currently available NISQ (noisy intermediate-scale quantum) devices. The high costs of using real quantum devices make it further challenging to research and develop quantum algorithms. As a result, performing classical simulations is usually the preferred method for researching and validating large-scale quantum algorithms. However, these simulations require a huge amount of resources, as each additional qubit exponentially increases the computational space required. Distributed Quantum Computing (DQC) is a promising alternative to reduce the resources required for simulating large quantum algorithms at the cost of increased runtime. This study presents a comparative analysis of two simulation methods: circuit-splitting and full-circuit execution using distributed memory, each having a different type of overhead. The first method, using CutQC, cuts the circuit into smaller subcircuits and allows us to simulate a large quantum circuit on smaller machines. The second method, using Qiskit-Aer-GPU, distributes the computational space across a distributed memory system to simulate the entire quantum circuit. Results indicate that full-circuit executions are faster than circuit-splitting for simulations performed on a single node. However, circuit-splitting simulations show promising results in specific scenarios as the number of qubits is scaled.
Executing large quantum circuits is not feasible using the currently available NISQ (noisy intermediate-scale quantum) devices. The high costs of using real quantum devices make it further challenging to research and develop quantum algorithms. As a result, performing classical simulations is usually the preferred method for researching and validating large-scale quantum algorithms. However, these simulations require a huge amount of resources, as each additional qubit exponentially increases the computational space required. Distributed Quantum Computing (DQC) is a promising alternative to reduce the resources required for simulating large quantum algorithms at the cost of increased runtime. This study presents a comparative analysis of two simulation methods: circuit-splitting and full-circuit execution using distributed memory, each having a different type of overhead. The first method, using CutQC, cuts the circuit into smaller subcircuits and allows us to simulate a large quantum circuit on smaller machines. The second method, using Qiskit-Aer-GPU, distributes the computational space across a distributed memory system to simulate the entire quantum circuit. Results indicate that full-circuit executions are faster than circuit-splitting for simulations performed on a single node. However, circuit-splitting simulations show promising results in specific scenarios as the number of qubits is scaled.
Today's Quantum Computers (QCs) face significant engineering challenges that limit their size and fidelity. To execute realistic applications, researchers must develop ways to move past these constraints. CutQC enables small QCs to run larger quantum circuits by cutting circuits into smaller subcircuits and then utilizing classical resources and Kronecker products to reproduce the desired output. In this work, we enhance the reconstruction process. In particular, we develop a distributed PyTorch implementation of CutQC's classical post-processing step, which can run across multiple nodes on either GPU or CPU devices. Our results show that our PyTorch implementation executes circuits of up to 35 qubits on 10- and 15-qubit QCs with efficient reconstruction. We use single-node computation as a baseline and then compare the results to the runtimes of our PyTorch workflows. By utilizing parallelism and specified devices, the reconstruction step of hybrid quantum-classical circuit execution can be improved. The original CutQC paper demonstrated a 60X to 8600X runtime speedup over classical simulation, and our work increases this speedup. These results show that large quantum circuits can be run on smaller QCs by leveraging circuit cutting with data parallelism techniques to maintain a reasonable runtime. This allows researchers to maintain the high fidelity of smaller machines while executing larger circuits.
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting — a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the limited quantum resource at hand — is used to mitigate these problems. However, classical postprocessing involved in circuit cutting generally grows exponentially with the number of cuts and quantum counts. This article introduces the notion of approximate circuit reconstruction. Using a sampling-based method like Markov Chain Monte Carlo (MCMC), we probabilistically select bit strings of high probability upon reconstruction. This avoids excessive calculations when reconstructing the full probability distribution. Our results show that such a sampling-based postprocessing method holds great potential for fast and reliable circuit reconstruction in the NISQ era and beyond.