Hybrid Quantum--Classical Pauli-Correlator Architecture for Image Reconstruction

Abstract

We introduce the Pauli-Correlator Autoencoder (PCAE), a hybrid quantum--classical architecture for image reconstruction. PCAE splits an image into patches and compresses each patch as a matrix product state (MPS). A small quantum circuit turns each compressed patch into a few measured numbers, and a classical neural network rebuilds the patch from these numbers and the patch position. A learnable energy term, taken from physics, is added to training and tracked as training proceeds. Two versions place the six qubits on a line (PCAE1D) or on a grid (PCAE2D). An averaging step makes the PCAE2D features follow rotations and reflections of the image exactly. Trained on one image at a time, PCAE2D rebuilds images from six public datasets with a peak signal-to-noise ratio of 25.8 to 41.6 decibels. On CIFAR-10 images not used in training, a formula-based stand-in for the PCAE2D features performs within 1 decibel of several simpler classical methods. Five trained models also run on real IBM quantum computers without retraining, and rebuild images at 25.90 to 31.52 decibels. A short argument and a synthetic test show that, with a linear final layer, measuring qubits in pairs is needed for targets built from products of inputs. These results show that PCAE works as a hybrid model that rebuilds varied images and runs on today's quantum hardware at the six-qubit scale.