Benchmarking Quantum Convolutional Neural Networks and their classical surrogates on long-range strongly correlated models

Abstract

We benchmark quantum convolutional neural networks (QCNNs) and their classical surrogates for phase differentiation in one-dimensional strongly correlated systems with beyond-nearest-neighbour terms. Using an anisotropic Heisenberg spin chain and an extended $t$-$t'$ Fermi-Hubbard model as representative spin and fermionic testbeds, we train QCNN classifiers on labelled ground-state datasets and map out finite-size phase diagrams. In hybrid setups, we employ Pauli backpropagation to express the QCNN measurement as a weighted sum of Pauli-string expectation values to be evaluated directly on input states, and study how truncation parameters control the trade-off between approximation accuracy and the size of the resulting Pauli expansion. Robust convergence is achieved for the Heisenberg model under aggressive truncation, whereas the Fermi-Hubbard model requires substantially looser thresholds, resulting in a sharp growth in retained Pauli strings and evaluation cost. Our results contribute to charting where hybrid quantum-classical training is viable for learning strongly correlated quantum states, and provide practical guidance for choosing truncation regimes in Pauli backpropagation-based surrogates.