Amplitude Ratios and Neural Network Quantum States

Vojtech Havlicek

IBM Quantum, IBM T.J. Watson Research Center

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Neural Network Quantum States (NQS) represent quantum wavefunctions by artificial neural networks. Here we study the wavefunction access provided by NQS defined in [Science, 355, 6325, pp. 602-606 (2017)] and relate it to results from distribution testing. This leads to improved distribution testing algorithms for such NQS. It also motivates an independent definition of a wavefunction access model: the amplitude ratio access. We compare it to sample and sample and query access models, previously considered in the study of dequantization of quantum algorithms. First, we show that the amplitude ratio access is strictly stronger than sample access. Second, we argue that the amplitude ratio access is strictly weaker than sample and query access, but also show that it retains many of its simulation capabilities. Interestingly, we only show such separation under computational assumptions. Lastly, we use the connection to distribution testing algorithms to produce an NQS with just three nodes that does not encode a valid wavefunction and cannot be sampled from.

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[1] Alessandro Sinibaldi, Clemens Giuliani, Giuseppe Carleo, and Filippo Vicentini, "Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution", Quantum 7, 1131 (2023).

[2] Sergey Bravyi, Giuseppe Carleo, David Gosset, and Yinchen Liu, "A rapidly mixing Markov chain from any gapped quantum many-body system", Quantum 7, 1173 (2023).

[3] Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim A. Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini, Lei Wang, Sebastian J. Wetzel, Giuseppe Carleo, Eliška Greplová, Roman Krems, Florian Marquardt, Michał Tomza, Maciej Lewenstein, and Alexandre Dauphin, "Modern applications of machine learning in quantum sciences", arXiv:2204.04198, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-21 17:41:20) and SAO/NASA ADS (last updated successfully 2024-05-21 17:41:21). The list may be incomplete as not all publishers provide suitable and complete citation data.