Power of Quantum Generative Learning

arXiv 2205.04730 ↗First posted 10 May 2022quant-ph cs.LGcited by 6

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Abstract (arXiv)

The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs). Despite the empirical achievements, the foundations and the potential advantages of QGLMs remain largely obscure. To narrow this knowledge gap, here we explore the generalization property of QGLMs, the capability to extend the model from learned to unknown data. We consider two prototypical QGLMs, quantum circuit Born machines and quantum generative adversarial networks, and explicitly give their generalization bounds. The result identifies superiorities of QGLMs over classical methods when quantum devices can directly access the target distribution and quantum kernels are employed. We further employ these generalization bounds to exhibit potential advantages in quantum state preparation and Hamiltonian learning. Numerical results of QGLMs in loading Gaussian distribution and estimating ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 49 of its 109 references that are in the map. First posted on arXiv 10 May 2022.

Builds on

49 of 109 references.

References · 49

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37 more

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2021Generalization in quantum machine learning from few training datacited by 214
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Cited by year

Citing papers per year: 2023: 4; 2024: 2.

6 papers.

2023On the Sample Complexity of Quantum Boltzmann Machine Learningcited by 18
2024Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuitscited by 7
2023Transition Role of Entangled Data in Quantum Machine Learningcited by 5
2023Hierarchical Learning for Quantum ML: Novel Training Technique for Large-Scale Variational Quantum Circuitscited by 5
2023Generative Invertible Quantum Neural Networkscited by 3
2024Exploring Biological Neuronal Correlations with Quantum Generative Modelscited by 0