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Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices

Marvin Bechtold, Johanna Barzen, Frank Leymann, Alexander Mandl, Julian Obst, Felix Truger, Benjamin Weder

Published Jan 1, 2023• 0 citations
Publisher
DOI
10.18419/opus-19807

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Abstract In the noisy intermediate-scale quantum (NISQ) era, quantum approximate optimisation algorithms are important tools for solving NP-hard problems such as combinatorial optimisation. However, most QAOA implementations ignore the inherent noise in quantum circuit environments. This study proposes a noisy quantum approximate optimisation algorithm (NQAOA) and analyses its performance under noisy conditions through numerical simulations. We compare the approximate ratios (AR) of various graphs under different optimisation strategies and noise conditions, and assess the impact of circuit depth, node count, edge count, and noise coefficient on the maximum cut (MaxCut). Experimental results show that noise leads to overfitting, and the approximate ratio ( AR ) exhibits fluctuating changes as the edge count e increases. The AR values under ideal conditions and the expected results are both superior to those under noisy conditions. This study is the first to systematically integrate multiple types of quantum noise into the QAOA framework, quantitatively analysing the synergistic effects of noise type, optimiser performance, and graph structure. Through theoretical derivations and numerical simulations, we established linear/exponential theoretical boundaries for AR decay related to noise coefficients, providing a critical reference for designing noise-resistant quantum optimisation algorithms on NISQ devices.
We investigate the Maximum Cut (MaxCut) problem on different graph classes with the quantum approximate optimization algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the approximation ratio achieved by a QAOA simulation are considered. To do so, we first solve the MaxCut problem on well-known graphs, then we consider simple and controllable perturbations of the graph and find again the approximate MaxCut with the QAOA. Through an analysis of the spectrum of the graphs and their perturbations, as well as a careful study of the associated automorphism groups, we aim to extract valuable insight into how symmetry impacts the performance of QAOA. These insights can then be leveraged to heuristically reduce the quantum circuit complexity, the number of training steps, or the number of parameters involved, thus enhancing the efficiency and effectiveness of QAOA-based solutions.