Quantum sequential scattering model for quantum state learning

• URL: http://arxiv.org/abs/2310.07797v1
• Date: Wed, 11 Oct 2023 18:31:40 GMT
• Title: Quantum sequential scattering model for quantum state learning
• Authors: Mingrui Jing, Geng Liu, Hongbin Ren, Xin Wang
• Abstract summary: We devise the quantum scattering model (QSSM) to overcome the vanishing problem to a large class of high-dimensional sequential target states possessing gradient-scaled Schmidt ranks. Our work has indicated 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.
• Score: 6.040584660207655
• License: http://creativecommons.org/licenses/by/4.0/
• 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 (QSSM), inspired by the classical diffusion model, to overcome this scalability issue. Training of our model could effectively circumvent the vanishing gradient problem to 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 physical and algorithmic meaningful quantum states and show an out-performance beating the conventional approaches in training speed and learning accuracy. Our work has indicated 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.

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