Parameterized quantum circuits as universal generative models for continuous multivariate distributions
Open accessAbstract
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.
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Parameterized quantum circuits have a significant ability to probe the Hilbert space.
“According to the interpretation of the operation of quantum gates as rotation of quantum states on the Bloch sphere, PQCs have a significant ability to probe the Hilbert space21,54.”
From Parameterized quantum random number generators for superconducting quantum hardware: novel architectures and NIST SP 800-22 evaluation under IBM noisy simulators (2026) · cites this paper as [54]
The Introduction and Results section on universal generators establish that certain parameterized quantum-circuit families are highly expressive: they can generate arbitrary target distributions within the stated support and accuracy conditions. Our copy does not characterize this as an ability to probe Hilbert space, nor does it ground that claim in Bloch-sphere rotations. No page numbers are available in the indexed passages. (LLM, conf=0.78)
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- Authors
- Barthe, A., Grossi, M., Vallecorsa, S., Tura, J., & Dunjko, V.
- Affiliations
- Leiden University (NL)
- European Organization for Nuclear Research (CH)
- Corresponding author
- Barthe, Alice
- Venue
- npj Quantum Information
- Published
- 2025-07-22
- Volume
- 11
- Issue
- 1
- Pages
- 121-121
- ISSN
- 2056-6387 (ISSN-L)
- PMC
- PMC12283343
- OpenAlex
- W4412545178
- Cited by
- 11
- References
- 27
- Citations by year
- 2026: 7 · 2025: 4
- FWCI
- 4.40
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- npj Quantum Information (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Leiden Repository (Leiden University) (submittedVersion, cc-by)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- European Space Agency (4000135723/21/I- DT-lr)
- European Union’s Horizon Europe (101040729, 101124342)
- Dutch Research Council (024.003.037)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- variational quantum circuits, quantum generative models, universality, Holevo bound, resource constraints, quantum advantage, quantum machine learning
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