Orbital expansion variational quantum eigensolver

Abstract

Variational Quantum Eigensolver~(VQE) has emerged as a promising method for investigating ground state properties in quantum chemistry, materials science, and condensed matter physics. However, the conventional VQE method generally lacks systematic improvement and convergence guarantees, particularly when dealing with strongly correlated systems. In light of these challenges, we present a novel framework called Orbital Expansion VQE (OE-VQE) to address these limitations. The key idea is to devise an efficient convergence path by utilizing shallower quantum circuits, starting from a highly compact active space and gradually expanding it until convergence to the ground state is achieved. To validate the effectiveness of the OE-VQE framework, we conducted benchmark simulations on several small yet representative molecules, including the $\rm H_{6}$ chain, $\rm H_{10}$ ring and $\rm N_2$. The simulation results demonstrate that our proposed convergence paths significantly enhance the performance of conventional VQE. Overall, our work sheds valuable insight into the simulation of molecules based on shallow quantum circuits, offering a promising avenue for advancing the efficiency and accuracy of VQE approaches in tackling complex molecular systems.

A resource-efficient quantum convolutional neural network

“…Hybrid quantum-classical machine learning models [17][18][19][20][21] based on the Variational Quantum Algorithm (VQA) [22][23][24][25][26] emerge as a notable advancement for designing QML algorithms with shallow-depth quantum circuits. A typical example is the Quantum Convolutional Neural Network (QCNN) [27], which is a quantum analog of the Convolutional Neural Network (CNN) [28,29] composed of the convolutional layer, the pooling layer, and the fully connected layer.…”