mlsanityData to 14 Oct 2026

Pseudo-dimension of quantum circuits

arXiv 2002.01490 ↗First posted 4 Feb 2020quant-ph cs.LGcited by 30

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Abstract (arXiv)

We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the upper bounds are polynomial in circuit depth and number of gates. Using these bounds, we exhibit a class of circuit output states out of which at least one has exponential state complexity, and moreover demonstrate that quantum circuits of known polynomial size and depth are PAC-learnable.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Feb 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 8; 2023: 7; 2024: 4; 2025: 2; 2026: 2.

30 papers.

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  1. 2021Generalization in quantum machine learning from few training datacited by 216
  2. 2022Exponential concentration in quantum kernel methodscited by 90
  3. 2021Encoding-dependent generalization bounds for parametrized quantum circuitscited by 82
  4. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
  5. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 49
  6. 2023A survey on the complexity of learning quantum statescited by 32
  7. 2021On the statistical complexity of quantum circuitscited by 25
  8. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 25
  9. 2021Structural risk minimization for quantum linear classifierscited by 24
  10. 2022Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrixcited by 23
  11. 2023Quantum Deep Hedgingcited by 22
  12. 2022High Dimensional Quantum Machine Learning With Small Quantum Computerscited by 18
18 more
  1. 2022Dynamical simulation via quantum machine learning with provable generalizationcited by 15
  2. 2023Learning quantum states and unitaries of bounded gate complexitycited by 15
  3. 2025A Primer on Quantum Machine Learningcited by 12
  4. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  5. 2023Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuitscited by 10
  6. 2021Effects of quantum resources on the statistical complexity of quantum circuitscited by 9
  7. 2022A kernel-based quantum random forest for improved classificationcited by 7
  8. 2023Classical Verification of Quantum Learningcited by 6
  9. 2024Unleashing the Expressive Power of Pulse-Based Quantum Neural Networkscited by 4
  10. 2024Entanglement-induced provable and robust quantum learning advantagescited by 4
  11. 2022A learning theory for quantum photonic processors and beyondcited by 3
  12. 2024Concept learning of parameterized quantum models from limited measurementscited by 3
  13. 2025Stability and Generalization of Quantum Neural Networkscited by 3
  14. 2026A PAC-Bayesian approach to generalization for quantum modelscited by 2
  15. 2021A Hybrid Quantum-Classical Hamiltonian Learning Algorithmcited by 1
  16. 2021Image Compression and Classification Using Qubits and Quantum Deep Learningcited by 1
  17. 2022Clifford Circuits can be Properly PAC Learned if and only if textsfRP=textsfNPcited by 1
  18. 2026A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learningcited by 0