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Efficient experimental validation of photonic boson sampling against the uniform distribution
N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvao, F. Sciarrino
TL;DR
Validating boson-sampling experiments is challenging when their output distributions are hard to simulate, and prior work questioned whether experimental data could be distinguished from a uniform distribution. This study applies statistical tests to photonic-chip data and reports successful validation against uniform sampling and discrimination of photon distinguishability.
Problem
The difficulty of simulating boson-sampling outputs also makes experimental validation challenging, with prior work questioning whether data could be distinguished from a uniform distribution.
Source: p. 1Method
The authors test photonic boson-sampling data against the uniform distribution using the Aaronson-Arkhipov test [8] and use a thresholded likelihood-ratio test to compare indistinguishable- and distinguishable-photon data.
Source: pp. 2, 5, Methods · p. 7Results
95% average success rate was reached with set sizes of about 100 events for the 5-, 7-, and 9-mode chips, and the test also worked with either reconstructed or ideal unitaries.
Source: pp. 3, 5Takeaways & Limitations
The experiments demonstrate feasibility of certifying boson-sampling data against the uniform distribution and alternative hypotheses, including distinguishable-photon data.
Source: pp. 2, 6The distinguishability test is not computationally efficient because it calculates probabilities for observed outcomes, though a laptop can test a small sample of up to about 25 photons in a day or so.
Source: p. 5
Abstract
from arXiv · showhide
A boson sampling device is a specialised quantum computer that solves a problem which is strongly believed to be computationally hard for classical computers. Recently a number of small-scale implementations have been reported, all based on multi-photon interference in multimode interferometers. In the hard-to-simulate regime, even validating the device's functioning may pose a problem . In a recent paper, Gogolin et al. showed that so-called symmetric algorithms would be unable to distinguish the experimental distribution from the trivial, uniform distribution. Here we report new boson sampling experiments on larger photonic chips, and analyse the data using a scalable statistical test recently proposed by Aaronson and Arkhipov. We show the test successfully validates small experimental data samples against the hypothesis that they are uniformly distributed. We also show how to discriminate data arising from either indistinguishable or distinguishable photons. Our results pave the way towards larger boson sampling experiments whose functioning, despite being non-trivial to simulate, can be certified against alternative hypotheses.
Methods
The methods combine integrated three-photon interferometers with two validation tests: one compares samples with the uniform distribution, and the other distinguishes indistinguishable- from distinguishable-photon data.
Interferometer fabrication and design
- The glass-chip interferometers were fabricated by femtosecond laser writing, while the 5-mode device implemented a Haar-random unitary and the 7- and 9-mode devices used random phases with balanced 50/50 couplers.The fabricated waveguides were single-mode at 800 nm, with about 0.5 dB/cm propagation losses.Source: Methods · p. 6
Experimental setup
- Three photons were generated by second-order parametric down-conversion, with a fourth photon serving as a trigger; source spectral correlations and possible six-photon events were included in expected distributions.The photons were spectrally filtered, polarization-compensated, and sent through delay lines before chip coupling.Source: Methods · p. 6
Validation against the uniform distribution
- For each no-collision outcome, the Aaronson-Arkhipov test [8] uses the interferometer unitary’s input-output submatrix to classify the event as boson-sampling or uniform, without calculating permanents.The test can be repeated across experimental outcomes, with majority voting for the final decision.Source: Methods · p. 6
Validation against distinguishable photons
- The distinguishability test adapts a likelihood-ratio test with thresholds for experimental noise, leaving near-equal probability ratios inconclusive and accumulating weighted evidence across outcomes.After N outcomes, the sign of D determines the dataset assignment; the analysis uses k1 = 0.9 and k2 = 1.5.Source: Methods · p. 7