Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability
Open accessAbstract
An active area of investigation in the search for quantum advantage is quantum machine learning. Quantum machine learning, and parameterized quantum circuits in a hybrid quantum-classical setup in particular, could bring advancements in accuracy by utilizing the high dimensionality of the Hilbert space as feature space. But is the ability of a quantum circuit to uniformly address the Hilbert space a good indicator of classification accuracy? In our work, we use methods and quantifications from prior art to perform a numerical study in order to evaluate the level of correlation. We find a moderate to strong correlation between the ability of the circuit to uniformly address the Hilbert space and the achieved classification accuracy for circuits that entail a single embedding layer followed by 1 or 2 circuit designs. This is based on our study encompassing 19 circuits in both 1- and 2-layer configurations, evaluated on 9 datasets of increasing difficulty. We also evaluate the correlation between entangling capability and classification accuracy in a similar setup, and find a weak correlation. Future work will focus on evaluating if this holds for different circuit designs.
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Existing cloud-based QRNGs implemented on NISQ devices often lack tunability and exhibit limited capacity to explore the Hilbert space, which directly reflects on their circuit expressibility.
“Existing cloud-based QRNGs implemented on NISQ devices often lack tunability and exhibit limited capacity to explore the Hilbert space, which directly reflects on their circuit expressibility.”
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 [21]
Section 3.1 and the Conclusion describe circuit expressibility in terms of a parameterized quantum circuit’s ability to uniformly address the Hilbert space. The paper does not establish that existing cloud-based QRNGs on NISQ devices lack tunability or have limited Hilbert-space reach; its experiments concern quantum classifiers, not QRNGs. The indexed passages provide section labels but no page numbers. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe limited circuit expressibility affects current QRNGs' ability to fully utilize circuit-based randomness potential by exploring the Hilbert space.
“Moreover, as mentioned, the limited circuit expressibility affects the current QRNGs’ ability to fully utilize the circuit-based randomness potential by exploring the Hilbert space21.”
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 [21]
Section 6 (Conclusion; page not provided) defines circuit expressibility in terms of a parameterized circuit’s ability to uniformly address the Hilbert space. The paper studies quantum classification, however, and does not establish that limited expressibility prevents current QRNGs from fully using circuit-based randomness potential. (LLM, conf=0.82)
Experimental — accuracy not yet measuredParameterized 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.”
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“Moreover, as mentioned, the limited circuit expressibility affects the current QRNGs’ ability to fully utilize the circuit-based randomness potential by exploring the Hilbert space 21 .”
- Authors
- Hubregtsen, T., Pichlmeier, J., Stecher, P., & Bertels, K.
- Affiliations
- BMW (Germany) (DE)
- Delft University of Technology (NL)
- Technical University of Munich (DE)
- Corresponding author
- Hubregtsen, Thomas
- Venue
- Quantum Machine Intelligence
- Published
- 2021-03-11
- Volume
- 3
- Issue
- 1
- ISSN
- 2524-4906 (ISSN-L)
- 2524-4914
- OpenAlex
- W3081750904
- Cited by
- 135
- References
- 34
- Citations by year
- 2026: 20 · 2025: 32 · 2024: 37 · 2023: 16 · 2022: 18 · 2021: 10 · 2020: 2
- FWCI
- 7.13
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Quantum Machine Intelligence (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- mediaTUM (Technical University of Munich) (submittedVersion, other-oa)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver (cc-by)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- variational quantum circuits, quantum machine learning, classification accuracy, expressibility, hybrid quantum-classical algorithms, quantum advantage
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