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Generative Quantum Machine Learning via Denoising Diffusion Probabilistic Models.

Bingzhi Zhang1,2, Peng Xu3, Xiaohui Chen4

  • 1Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.

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Summary
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We introduce the quantum denoising diffusion probabilistic model (QuDDPM) for efficient quantum data generation. This model avoids training issues and effectively learns complex quantum data, including noise models and many-body phases.

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Generative Models

Background:

  • Deep generative models, including denoising diffusion probabilistic models (DDPMs), are crucial for tasks like computer vision and natural language processing.
  • Quantum generative models leverage quantum phenomena like entanglement and superposition for learning quantum data.
  • Current quantum generative models face challenges in efficient training and expressivity.

Purpose of the Study:

  • To propose a Quantum Denoising Probabilistic Model (QuDDPM) for efficient and versatile generative learning of quantum data.
  • To address training inefficiencies and the barren plateau problem in quantum generative models.
  • To demonstrate the model's capability in learning complex quantum data structures.

Main Methods:

  • Developed QuDDPM inspired by classical DDPMs, incorporating sufficient circuit layers for expressivity.
  • Introduced intermediate training tasks as interpolation between target quantum data distribution and noise.
  • Analyzed learning error bounds and validated the model on various quantum data learning tasks.

Main Results:

  • QuDDPM demonstrates efficient trainability by avoiding the barren plateau problem.
  • The model successfully learns correlated quantum noise models.
  • QuDDPM effectively captures quantum many-body phases and the topological structure of quantum data.

Conclusions:

  • QuDDPM offers a versatile and efficient paradigm for quantum generative learning.
  • The proposed method enables high-quality generation and learning of complex quantum data.
  • This work paves the way for advanced applications of generative models in quantum information science.