aiqbench analysis
This paper proposes a hybrid approach to the graph isomorphism problem by deriving a classical algorithm that leverages statistical properties from Gaussian boson samplers to efficiently rule out non-isomorphic graphs. The authors critically assess this method against established benchmarks, including the classical color refinement and Babai's quasi-polynomial algorithm, within the constraints of the current NISQ era. The work highlights the potential for extracting practical utility from noisy quantum systems even before full quantum advantage is demonstrated.
A Quantum-Inspired Algorithm for Graph Isomorphism
arXiv:2512.24423v3 Announce Type: replace Abstract: The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical quantum advantage remain elusive in this era, it provides space to develop and analyze the advantages and limitations of systems and their ability to solve problems. In this work, we critically assess a proposed quantum algorithm for the graph isomorphism problem, implemented on a photonic quantum device. Inspired by the nature of this quantum algorithm, we formulate a necessary condition for the isomorphism of graphs encoded in Gaussian boson samplers and a classical algorithm to test for it. Our classical algorithm makes use of efficiently computable statistical properties of a quantum sampling system to show a pair of graphs fail to meet our necessary condition and thus cannot be isomorphic. We analyze our algorithm in the context of the inspiring, sampler-based quantum algorithm of Br\`adler et. al., the classical color refinement algorithm, and the state-of-the-art quasi-polynomial Babai algorithm.
Abstract:The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical quantum advantage remain elusive in this era, it provides space to develop and analyze the advantages and limitations of systems and their ability to solve problems. In this work, we critically assess a proposed quantum algorithm for the graph isomorphism problem, implemented on a photonic quantum device. Inspired by the nature of this quantum algorithm, we formulate a necessary condition for the isomorphism of graphs encoded in Gaussian boson samplers and a classical algorithm to test for it. Our classical algorithm makes use of efficiently computable statistical properties of a quantum sampling system to show a pair of graphs fail to meet our necessary condition and thus cannot be isomorphic. We analyze our algorithm in the context of the inspiring, sampler-based quantum algorithm of Bràdler et. al., the classical color refinement algorithm, and the state-of-the-art quasi-polynomial Babai algorithm.
arXiv:2512.24423 [quant-ph]
(or arXiv:2512.24423v3 [quant-ph] for this version)
Full text under the publisher's open licence · 179 words
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