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Evaluating Quantum Wire Cutting for QAOA: Performance Benchmarks in Ideal and Noisy Environments

Michel Meulen, Niels M. P. Neumann, Jasper Verbree

TL;DR

The paper tackles running larger quantum circuits on NISQ devices by circuit cutting, with a focus on wire-cutting variants. It systematically compares three wire-cutting strategies—exact Pauli-based cuts, randomized Clifford measurements, and randomized Pauli rotations—and applies the best-performing approach to QAOA for MaxCut. Key findings show randomized Clifford-based wire cutting reduces sampling overhead and improves performance in ideal simulations, but its advantage diminishes in noisy settings and as the number of cuts grows. The work highlights practical trade-offs between qubit reduction and algorithm accuracy, suggesting future work on larger sample sizes, hardware experiments, and error-mitigation techniques to reclaim performance in realistic environments.

Abstract

Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these techniques called quantum circuit cutting. With circuit cutting, a quantum circuit is decomposed into smaller sub-circuits, each of which can be run on smaller quantum hardware. We compare the performance of quantum circuit cutting with different cutting strategies, and then apply circuit cutting to a QAOA algorithm. Using simulations, we first show that Randomized Clifford measurements outperform both Pauli and random unitary measurements. Second, we show that circuit cutting has trouble providing correct answers in noisy settings, especially as the number of circuits increases.

Evaluating Quantum Wire Cutting for QAOA: Performance Benchmarks in Ideal and Noisy Environments

TL;DR

The paper tackles running larger quantum circuits on NISQ devices by circuit cutting, with a focus on wire-cutting variants. It systematically compares three wire-cutting strategies—exact Pauli-based cuts, randomized Clifford measurements, and randomized Pauli rotations—and applies the best-performing approach to QAOA for MaxCut. Key findings show randomized Clifford-based wire cutting reduces sampling overhead and improves performance in ideal simulations, but its advantage diminishes in noisy settings and as the number of cuts grows. The work highlights practical trade-offs between qubit reduction and algorithm accuracy, suggesting future work on larger sample sizes, hardware experiments, and error-mitigation techniques to reclaim performance in realistic environments.

Abstract

Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these techniques called quantum circuit cutting. With circuit cutting, a quantum circuit is decomposed into smaller sub-circuits, each of which can be run on smaller quantum hardware. We compare the performance of quantum circuit cutting with different cutting strategies, and then apply circuit cutting to a QAOA algorithm. Using simulations, we first show that Randomized Clifford measurements outperform both Pauli and random unitary measurements. Second, we show that circuit cutting has trouble providing correct answers in noisy settings, especially as the number of circuits increases.
Paper Structure (12 sections, 4 equations, 5 figures, 1 table)

This paper contains 12 sections, 4 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Wire cutting
  3. Experimental setup
  4. Comparing circuit cutting methods
  5. Evaluating the performance for circuit cutting in QAOA
  6. Code framework
  7. Results
  8. Wire cutting techniques
  9. Wire cutting QAOA for MaxCut
  10. Ideal Simulations
  11. Noisy Simulations
  12. Conclusion

Figures (5)

  • Figure 1: Visual representation of wire cutting using Pauli measurements. Each subcircuit is run on a quantum device and the results are classically recombined. The tensor product symbol ($\otimes$) refers to the recombination of the different probability distributions as in Equation \ref{['eq:pauli_wire_cut']}.
  • Figure 2: Visual representation of randomized-measurement-based wire cutting. For every sample, the method randomly chooses between two quantum channels: The random Clifford channel (top) and the depolarization channel (bottom). The chosen channel is then executed on a hybrid-quantum-classical-device. The recombination of the probabilities follows Equation \ref{['eq:randomized_cutting_prob']}.
  • Figure 3: Visual representation of the used layered graphs.
  • Figure 4: Total Hellinger distance averaged over 60 independent runs for three wire cutting techniques (Pauli Wire Cut, Random Wire Cut with Random Clifford, and Random Wire Cut with Random Rotation) across varying shot budgets.
  • Figure 5: Numerical results on the performance of circuit cutting for QAOA. The left figures show results using uncut circuits, and the right figures show results using circuit cutting. Each bar shows the fraction of best, second best, third best, and wrong answer measured three graph instances and different shot budgets.