arXiv:2310.07797 · Physical Review A

Quantum sequential scattering model for quantum state learning

Mingrui Jing, Geng Liu, Hongbin Ren, Xin Wang

Published Jun 18, 2024• 1 citation

Abstract

Learning probability distribution is an essential framework in classical learning theory. As a counterpart, quantum state learning has spurred the exploration of quantum machine learning theory. However, as dimensionality increases, learning a high-dimensional unknown quantum state via conventional quantum neural network approaches remains challenging due to trainability issues. In this work we devise the quantum sequential scattering model, inspired by the classical diffusion model, to overcome this scalability issue. Training of our model could effectively circumvent the vanishing gradient problem for a large class of high-dimensional target states possessing polynomial-scaled Schmidt ranks. Theoretical analysis and numerical experiments provide evidence for our model's effectiveness in learning both physically and algorithmically meaningful quantum states and outperform the conventional approaches in training speed and learning accuracy. Our work indicates that an increasing entanglement (a property of quantum states) in the target states necessitates a larger-scaled model, which could reduce our model's learning performance and efficiency.

DOI: 10.1103/physreva.109.062425

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