Quantum Super-resolution by Adaptive Non-local Observables

TL;DR

This paper tackles image super-resolution by introducing Adaptive Non-Local Observable Variational Quantum Circuits (ANO-VQCs). The method jointly learns circuit parameters and trainable non-local Hermitian observables, enabling measurements that span multi-qubit subspaces and access richer information in the high-dimensional Hilbert space. The approach frames SR as a quantum learning task with a loss combining pixel fidelity and perceptual similarity, and demonstrates, on MNIST, that 3-local observables yield lower MSE and higher PSNR/SSIM than 2-local counterparts, with a modest LPIPS trade-off. The work presents a first study of quantum circuits for SR and shows that adaptive measurements can significantly boost reconstruction quality with relatively small models, suggesting a promising direction for resource-efficient quantum vision tasks.

Abstract

Super-resolution (SR) seeks to reconstruct high-resolution (HR) data from low-resolution (LR) observations. Classical deep learning methods have advanced SR substantially, but require increasingly deeper networks, large datasets, and heavy computation to capture fine-grained correlations. In this work, we present the \emph{first study} to investigate quantum circuits for SR. We propose a framework based on Variational Quantum Circuits (VQCs) with \emph{Adaptive Non-Local Observable} (ANO) measurements. Unlike conventional VQCs with fixed Pauli readouts, ANO introduces trainable multi-qubit Hermitian observables, allowing the measurement process to adapt during training. This design leverages the high-dimensional Hilbert space of quantum systems and the representational structure provided by entanglement and superposition. Experiments demonstrate that ANO-VQCs achieve up to five-fold higher resolution with a relatively small model size, suggesting a promising new direction at the intersection of quantum machine learning and super-resolution.

Figures (4)

• Figure 1: A VQC diagrm of (\ref{['E: encoding V']}), (\ref{['E: variational U']}), which is also implemented in Sec. \ref{['sec_exp_results']}. The variational block represented by a pink box is repeated $L$ times to increase the circuit depth.
• Figure 2: Let $\mathbb{H}(n)$ denote the space of all observables represented by ANO. The conventional VQC with fixed Pauli measurements becomes a special case (an equivalent subclass) within the ANO function classes; see lin2025ano for details.
• Figure 3: ANO-VQC for SR. An LR input $x$ is encoded by $V(x)$ into state $V(x)\ket{\psi_0}$, transformed by variational layers $U(\theta)$, and finally measured by an adaptive $k$-local observable $H(\phi)$ to reconstruct the HR output.
• Figure 4: Super-resolution with 3-local ANO–VQC: $4 \times 4$ LR digit inputs (top) are reconstructed into $12 \times 12$, $16 \times 16$, and $20 \times 20$ HR outputs in the second, third, and fourth rows.