Quantum Graph Neural Networks

TL;DR

Quantum Graph Neural Networks (QGNNs) introduce a graph-aware variational quantum framework for processing graph-structured quantum data on distributed quantum systems. The authors define a general QGNN Ansatz and three specialized architectures—qgrnn, qgcnn, and qsgcnn—demonstrating their applicability to learning Hamiltonian dynamics, entanglement generation in sensor networks, spectral clustering, and graph isomorphism. Through four numerical experiments, QGNNs show the ability to capture graph-structured quantum processes and offer practical paths for near-term quantum devices, including CV implementations and low-qubit precision regimes. The work outlines future directions such as incorporating quantum degrees of freedom on edges, quantum-phase backpropagation, and extensions to richer graph representations relevant for quantum chemistry and beyond.

Abstract

We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed quantum systems over a quantum network. Along with this general class of ansatze, we introduce further specialized architectures, namely, Quantum Graph Recurrent Neural Networks (QGRNN) and Quantum Graph Convolutional Neural Networks (QGCNN). We provide four example applications of QGNNs: learning Hamiltonian dynamics of quantum systems, learning how to create multipartite entanglement in a quantum network, unsupervised learning for spectral clustering, and supervised learning for graph isomorphism classification.

Figures (4)

• Figure 1: Left: Batch average infidelity with respect to ground truth state sampled at 15 randomly chosen times of quantum Hamiltonian evolution. We see the initial guess has a densely connected topology and the qgrnn learns the ring structure of the true Hamiltonian. Right: Ising Hamiltonian parameters (weights & biases) on a color scale.
• Figure 2: Left: Stabilizer Hamiltonian expectation and fidelity over training iterations. A picture of the quantum network topology is inset. Right: Quantum phase kickback test on the learned GHZ state. We observe a $7$x boost in Rabi oscillation frequency for a 7-node network, thus demonstrating we have reached the Heisenberg limit of sensitivity for the quantum sensor network.
• Figure 3: qsgcnn spectral clustering results for 5-qubit precision (top) with quartic double-well potential and 1-qubit precision (bottom) for different graphs. Weight values are represented as opacity of edges, output sampled node values as grayscale. Lower precision allows for more nodes in the simulation of the quantum neural network. The graphs displayed are the most probable (populated) configurations, and to their right is the output probability distribution over potential energies. We see lower energies are most probable and that these configurations have node values clustered.
• Figure 4: Graph isomorphism loss curves for training and validation for various numbers of samples. Left is for 6 node graphs and right is for 15 node graphs. The loss is based on the Kolmogorov-Smirnov statistic comparing the sampled distribution of energies of the qgcnn output on two graphs.