# Quantum Super-resolution by Adaptive Non-local Observables

arXiv: https://arxiv.org/abs/2601.14433 · HTML: https://mlsanity.com/paper/2601.14433/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusion](https://mlsanity.com/paper/2203.12621/) (2022)
- [EDiffSR: An Efficient Diffusion Probabilistic Model for Remote Sensing Image Super-Resolution](https://mlsanity.com/paper/2310.19288/) (2023)
- [Learning to Measure Quantum Neural Networks](https://mlsanity.com/paper/2501.05663/) (2025)
- [Adaptive Non-local Observable on Quantum Neural Networks](https://mlsanity.com/paper/2504.13414/) (2025)

## Built on by (most cited first, 4 of 4)

- [Multivariate Time Series Forecasting with Adaptive Non-Local Observables](https://mlsanity.com/paper/2607.24399/) (2026)
- [Enhancing Quantum Diffusion Models for Complex Image Generation](https://mlsanity.com/paper/2602.03405/) (2026)
- [Diagonal Adaptive Non-local Observables on Quantum Neural Networks](https://mlsanity.com/paper/2605.15410/) (2026)
- [Learning to Program Adaptive Non-Local Observables for Machine Learning](https://mlsanity.com/paper/2609.18655/) (2026)

## Abstract (arXiv)

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 first study to investigate quantum circuits for SR. We propose a framework based on Variational Quantum Circuits (VQCs) with 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.