Linear cross-entropy certification of quantum computational advantage in Gaussian Boson Sampling
Abstract: Validation of quantum advantage claims in the context of Gaussian Boson Sampling (GBS) currently relies on providing evidence that the experimental samples genuinely follow their corresponding ground truth, i.e., the theoretical model of the experiment that includes all the possible losses that the experimenters can account for. This approach to verification has an important drawback: it is necessary to assume that the ground truth distributions are computationally hard to sample, that is, that they are sufficiently close to the distribution of the ideal, lossless experiment, for which there is evidence that sampling, either exactly or approximately, is a computationally hard task. This assumption, which cannot be easily confirmed, opens the door to classical algorithms that exploit the noise in the ground truth to efficiently simulate the experiments, thus undermining any quantum advantage claim. In this work, we argue that one can avoid this issue by validating GBS implementations using their corresponding ideal distributions directly. We explain how to use a modified version of the linear cross-entropy, a measure that we call the LXE score, to find reference values that help us assess how close a given GBS implementation is to its corresponding ideal model. Finally, we analytically compute the score that would be obtained by a lossless GBS implementation.
- D. Hangleiter and J. Eisert, Computational advantage of quantum random sampling, Reviews of Modern Physics 95, 035001 (2023).
- N. Quesada, J. M. Arrazola, and N. Killoran, Gaussian boson sampling using threshold detectors, Physical Review A 98, 062322 (2018).
- S. Aaronson and A. Arkhipov, The computational complexity of linear optics, in Proceedings of the forty-third annual ACM symposium on Theory of computing (2011) pp. 333–342.
- D. Hangleiter, M. Kliesch, J. Eisert, and C. Gogolin, Sample complexity of device-independently certified “quantum supremacy”, Physical review letters 122, 210502 (2019).
- Y. Cardin and N. Quesada, Photon-number moments and cumulants of gaussian states, arXiv preprint arXiv:2212.06067 (2022).
- J. Martínez-Cifuentes, K. Fonseca-Romero, and N. Quesada, Classical models may be a better explanation of the jiuzhang 1.0 gaussian boson sampler than its targeted squeezed light model, Quantum 7, 1076 (2023).
- C. Oh, L. Jiang, and B. Fefferman, Spoofing cross-entropy measure in boson sampling, Physical Review Letters 131, 010401 (2023a).
- A. M. Dalzell, N. Hunter-Jones, and F. G. Brandão, Random quantum circuits transform local noise into global white noise, arXiv preprint arXiv:2111.14907 (2021).
- B. Collins, S. Matsumoto, and J. Novak, The weingarten calculus, arXiv preprint arXiv:2109.14890 (2022).
- A. Serafini, Quantum continuous variables: a primer of theoretical methods (CRC press, 2017).
- A. Barvinok, Combinatorics and complexity of partition functions, Vol. 30 (Springer, 2016).
- M. Ledoux, The concentration of measure phenomenon, 89 (American Mathematical Soc., 2001).
- L. Comtet, Advanced Combinatorics: The art of finite and infinite expansions (Springer Science & Business Media, 1974).
- P. Flajolet and R. Sedgewick, Analytic combinatorics (cambridge University press, 2009).
- S. Matsumoto, General moments of matrix elements from circular orthogonal ensembles, Random Matrices: Theory and Applications 1, 1250005 (2012).
- F. Roberts and B. Tesman, Applied combinatorics (CRC Press, 2009).
- H. S. Wilf, generatingfunctionology (CRC press, 2005).
- B. Collins and P. Śniady, Integration with respect to the haar measure on unitary, orthogonal and symplectic group, Communications in Mathematical Physics 264, 773 (2006).
- A. Islami, Symmetric Functions as Characters of Hyperoctahedral Group, Ph.D. thesis, York University (2020).
- V. Kocharovsky, V. V. Kocharovsky, and S. Tarasov, Atomic boson sampling in a bose-einstein-condensed gas, Physical Review A 106, 063312 (2022).
- S. Rahimi-Keshari, A. P. Lund, and T. C. Ralph, What can quantum optics say about computational complexity theory?, Physical review letters 114, 060501 (2015).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.