Note on the Universality of Parameterized IQP Circuits with Hidden Units for Generating Probability Distributions

• URL: http://arxiv.org/abs/2504.05997v1
• Date: Tue, 08 Apr 2025 13:03:23 GMT
• Title: Note on the Universality of Parameterized IQP Circuits with Hidden Units for Generating Probability Distributions
• Authors: Andrii Kurkin, Kevin Shen, Susanne Pielawa, Hao Wang, Vedran Dunjko,
• Abstract summary: An interesting quantum generative model based on parameterized instantaneous quantum (IQP) circuits has emerged.<n>The model is proven not to be universal for generating arbitrary distributions, but it is suspected that marginals can be - much like Boltzmann machines achieve universality by utilizing hidden layers.
• Score: 4.778142132143664
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only on the expectation values of observables of the model. The model is proven not to be universal for generating arbitrary distributions, but it is suspected that marginals can be - much like Boltzmann machines achieve universality by utilizing hidden (traced-out in quantum jargon) layers. In this short note, we provide two simple proofs of this fact. The first is near-trivial and asymptotic, and the second shows universality can be achieved with a reasonable number of additional qubits.

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