The Quantum-like Behavior of Neural Networks

Stephen Allan Selesnick, Gualtiero Piccinini

Haoxiang Chen, Weiluo Ren, Xiang Li +1 more

One-dimensional (1D) systems and models provide a versatile platform for emergent phenomena induced by strong electron correlation. In this work, we extend the newly developed real space neural network quantum Monte Carlo methods to study the quantum phase transition of electronic and magnetic properties. Hydrogen chains of different interatomic distances are explored systematically with both open and periodic boundary conditions, and fully correlated ground state many-body wavefunction is achieved via unsupervised training of neural networks. We demonstrate for the first time that neural networks are capable of capturing the quantum critical behavior of Tomonaga- Luttinger liquid (TLL), which is known to dominate 1D quantum systems. Moreover, we reveal the breakdown of TLL phase and the emergence of a Fermi liquid behavior, evidenced by abrupt changes in the spin structure and the momentum distribution. Such behavior is absent in commonly studied 1D lattice models and is likely due to the involvement of high-energy orbitals of hydrogen atoms. Our work highlights the powerfulness of neural networks for representing complex quantum phases.

秀稔 西森, Hidetoshi Nishimori, Yoshihiko Nonomura

Jincheng Zhang

Quantum Adaptive Neural Network Model represents a novel approach to neural network architecture leveraging quantum phenomena to enhance expressiveness and computational efficiency. Traditional neural networks often struggle with limitations in handling complex data and achieving optimal performance. This research proposes a quantum-enhanced neural network model, employing quantum machine learning techniques to overcome these limitations. The core mechanism centers around mimicking neural network behavior using quantum simulations, with subsequent optimization driven by quantum algorithms. This work aims to demonstrate a significant improvement in model accuracy and potentially accelerate training times, offering a compelling advancement in the field of artificial intelligence. We explore the potential of quantum-enhanced neural networks to address challenges inherent in large-scale data processing and complex pattern recognition.

Moolchand Sharma, Nebojša Bačanin, Tarik Ahmed Rashid

Do Ngoc Diep