Statistical Analysis of Quantum State Learning Process in Quantum Neural Networks

This GitHub repository contains a demonstration for the main theorem verification and practical variational state learning examples. Please refer to our paper on Section.4 for further information.

Install Paddle Quantum and Tensorcircuit

The experiment is carried in Paddle Quantum version 2.3.0 and Tensorcircuit version 0.8.0. To run the codes in this repository, you need to install Paddle Quantum and Tensorcircuit first.

pip install paddle-quantum==2.3.0
pip install tensorcircuit==0.8.0

File Description

training_landscapes demonstrates the training landscape profiles in Fig.3 by sampling from p-overlap states as well as different optimization directions.

pr_local_minima provides the code for directly verifying the exponentially likely local minima proposed by Theorem 2 in Fig. 4 in terms of the number of qubits, the number of trainable parameters, and overlap information.

state_learning provides the code for the varational training of quantum neural networks on the state learning task shown in Fig. 1(c) beginning with initial 0.8-overlap states.

utils.py includes helper functions.