Parameterized quantum circuits as universal generative models for continuous multivariate distributions
arxiv(2024)
Abstract
Parameterized quantum circuits have been extensively used as the basis for
machine learning models in regression, classification, and generative tasks.
For supervised learning, their expressivity has been thoroughly investigated
and several universality properties have been proven. However, in the case of
quantum generative modelling, much less is known, especially when the task is
to model distributions over continuous variables. In this work, we elucidate
expectation value sampling-based models. Such models output the expectation
values of a set of fixed observables from a quantum circuit into which
classical random data has been uploaded. We prove the universality of such
variational quantum algorithms for the generation of multivariate
distributions. We explore various architectures which allow universality and
prove tight bounds connecting the minimal required qubit number, and the
minimal required number of measurements needed. Our results may help guide the
design of future quantum circuits in generative modelling tasks.
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