Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model

Javier Martínez-Cifuentes1, K. M. Fonseca-Romero2, and Nicolás Quesada1

1Department of Engineering Physics, École Polytechnique de Montréal, Montréal, QC, H3T 1JK, Canada
2Departamento de Física, Universidad Nacional de Colombia - Sede Bogotá, Facultad de Ciencias, Grupo de Óptica e Información Cuántica, Carrera 30 Calle 45-03, C.P. 111321, Bogotá, Colombia

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Recently, Zhong et al. [1, 2] performed landmark Gaussian boson sampling experiments with up to 144 modes using threshold detectors. The authors claim to have achieved quantum computational advantage with the implementation of these experiments, named Jiuzhang 1.0 and Jiuzhang 2.0. Their experimental results are validated against several classical hypotheses and adversaries using tests such as the comparison of statistical correlations between modes, Bayesian hypothesis testing and the Heavy Output Generation (HOG) test. In this work we propose an alternative classical hypothesis for the validation of these experiments. We use the probability distribution of mixtures of coherent states sent into a lossy interferometer; these input mixed states, which we term $\textit{squashed states}$, have vacuum fluctuations in one quadrature and excess fluctuations in the other. We find that for configurations in the high photon number density regime, the comparison of statistical correlations does not tell apart the ground truth of the experiment (two-mode squeezed states sent into an interferometer) from our alternative hypothesis. On the other hand, the Bayesian test indicates that, for all configurations excepting Jiuzhang 1.0, the ground truth is a more likely explanation of the experimental data than our alternative hypothesis. A similar result is obtained for the HOG test: for all configurations of Jiuzhang 2.0, the test indicates that the experimental samples have higher ground truth probability than the samples obtained from our alternative distribution; for Jiuzhang 1.0 the test is inconclusive. Our results provide a new hypothesis that should be considered in the validation of future GBS experiments, and shed light into the need to identify proper metrics to verify quantum advantage in the context of threshold GBS. Additionally, they indicate that a classical explanation of the Jiuzhang 1.0 experiment, lacking any quantum features, has not been ruled out.

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