Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Kaposi, Ágoston; Kolarovszki, Zoltán; Kozsik, Tamás; Zimborás, Zoltán; Rakyta, Péter

doi:10.48550/arxiv.2109.04528

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…We do not conjecture that these complexities are optimal. The structure of this matrix function may be exploited to reduce the complexity, for example by using methods similar to those for low rank permanents [22], exploiting recursion [24] and using Laplace expansions [25]. However, we leave it as an open problem to find faster algorithms for the Bristolian.…”

Section: Time Complexitiesmentioning

confidence: 99%

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Threshold detection statistics of bosonic states

Bulmer¹,

Paesani²,

Chadwick³

et al. 2022

Preprint

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In quantum photonics, threshold detectors, distinguishing between vacuum and one or more photons, such as superconducting nanowires and avalanche photodiodes, are routinely used to measure Fock and Gaussian states of light. Despite being the standard measurement scheme, there is no general closed form expression for measurement probabilities with threshold detectors, unless accepting coarse approximations or combinatorially scaling summations. Here, we present new matrix functions to fill this gap. We develop the Bristolian and the loop Torontonian functions for threshold detection of Fock and displaced Gaussian states, respectively, and connect them to each other and to existing matrix functions. By providing a unified picture of bosonic statistics for most quantum states of light, we provide novel tools for the design and analysis of photonic quantum technologies.

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Section: Time Complexitiesmentioning

confidence: 99%

“…However, both of these steps can make use of the Cholesky decomposition of O, so we anticipate that the polynomial prefactor can be improved, following the methods described in Ref. [24].…”

Section: Time Complexitiesmentioning

confidence: 99%

Threshold detection statistics of bosonic states

Bulmer¹,

Paesani²,

Chadwick³

et al. 2022

Preprint

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

Martínez-Cifuentes

Romero

Quesada

2023

Quantum

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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 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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Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Cited by 2 publications

References 33 publications

Threshold detection statistics of bosonic states

Threshold detection statistics of bosonic states

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

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