Parameterized quantum circuits as universal generative models for continuous multivariate distributions

npj Quantum Information, vol. 11, pp. 121

Abstract

Parameterized quantum circuits are a key component of quantum machine learning models for regression, classification, and generative tasks. Quantum Circuit Born machines produce discrete distributions over bitstrings whose length is exactly the number of qubits. To allow for distributions on continuous variables, new models have been introduced where classical randomness is uploaded into quantum circuits and expectation values are returned with a dimensionality decoupled from qubit number. While these models have been explored experimentally, their expressivity remains underexplored. In this work, we formalize this family and establish its theoretical foundation. We prove the universality of several variational circuit architectures for generating continuous multivariate distributions and derive tight resource bounds to reach universality using tools related to the Holevo bound. Our results reveal a trade-off between the number of qubits and measurements. We further explore relaxed notions of universality and present a practical use case, outlining potential domains for quantum advantage.

Authors 5

1. Alice Barthe corresponding Aachen applied Quantum algorithms (aQa) Instituut-Lorentz

   Leiden University · European Organization for Nuclear Research

   Affiliation as printed

   Applied Quantum Algorithms, Universiteit Leiden, Leiden, the Netherlands

   Instituut-Lorentz, Universiteit Leiden, Leiden, the Netherlands

   Quantum Technology Initiative, CERN, Geneva, Switzerland

2. Michele Grossi

   European Organization for Nuclear Research

   Affiliation as printed

   Quantum Technology Initiative, CERN, Geneva, Switzerland

3. Sofia Vallecorsa

   European Organization for Nuclear Research

   Affiliation as printed

   Quantum Technology Initiative, CERN, Geneva, Switzerland

4. Jordi Tura Aachen applied Quantum algorithms (aQa) Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Applied Quantum Algorithms, Universiteit Leiden, Leiden, the Netherlands

   Instituut-Lorentz, Universiteit Leiden, Leiden, the Netherlands

5. Vedran Dunjko Aachen applied Quantum algorithms (aQa) Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Applied Quantum Algorithms, Universiteit Leiden, Leiden, the Netherlands

   Instituut-Lorentz, Universiteit Leiden, Leiden, the Netherlands