Quantum Super-Resolution Achieves High-Resolution Data from Low-Resolution Observations

Researchers are tackling the long-standing problem of super-resolution imaging, aiming to create detailed images from blurry, low-resolution data. Hsin-Yi Lin from Seton Hall University, Huan-Hsin Tseng and Shinjae Yoo from Brookhaven National Laboratory, along with Samuel Yen-Chi Chen, present the first investigation into utilising quantum circuits for this task, potentially bypassing the need for massive datasets and intensive computation required by traditional machine learning approaches. Their innovative framework employs Variational Quantum Circuits with Adaptive Non-Local Observable (ANO) measurements, allowing the quantum system to learn and refine the image reconstruction process itself. This novel design, leveraging quantum entanglement and superposition, achieves up to five-fold higher resolution with a remarkably small model , signalling a significant leap forward at the exciting intersection of quantum machine learning and image processing.

Researchers engineered these ANOs to adapt during training, effectively allowing the measurement process itself to learn and refine its ability to extract high-resolution information. This adaptation is inspired by the Heisenberg picture, treating measurement operators as trainable entities, expanding the representational capacity of the quantum neural network and enabling richer qubit interactions. The team specifically designed ANOs to act on multiple qubits simultaneously, facilitating the capture of fine-grained correlations crucial for SR.

Experiments employed ANO-VQCs to achieve up to five-fold higher resolution compared to existing methods, all while maintaining a relatively small model size. Data was encoded into the quantum system, processed through the VQC, and then measured using the adaptive ANOs, generating outputs that were subsequently decoded to reconstruct the high-resolution image. This process was iteratively refined through training, minimizing the difference between the reconstructed HR image and the ground truth. Crucially, the team demonstrated that non-local observables function as effective “lenses” within the quantum system, extracting subtle details from entangled multi-qubit subspaces. This innovative method leverages the inherent dimensionality of quantum Hilbert space to achieve perceptual improvements in SR without the need for excessively deep circuits or large qubit counts. Experiments were conducted utilising the MNIST dataset, consisting of 28 × 28 grayscale images, downsampled to 4 × 4 pixels and then upscaled to target resolutions of 12 × 12, 16 × 16, and 20 × 20. The team measured quantitative metrics including Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) to rigorously evaluate the performance of the ANO-VQC models.
Results demonstrate that the 3-local ANO-VQC consistently outperformed the 2-local counterpart, achieving lower MSE and higher PSNR and SSIM values across all scaling factors, indicating more accurate pixel-level reconstruction. Specifically, for the ×3 super-resolution task, the 3-local model reached an MSE of 0.35 and an SSIM of 0.87, compared to 0.42 and 0.84 for the 2-local variant. Tests prove that deeper non-local observables enhance reconstruction fidelity, although a slight increase in LPIPS values suggests a modest perceptual trade-off , sharper details may appear less natural. The researchers recorded that as the scaling factor increased to ×5, both models exhibited gradual degradation in reconstruction quality, a predictable outcome with higher upsampling ratios.

Measurements confirm that by allowing multi-qubit Hermitian observables to adapt during training, the model effectively explores a richer subspace of the Hilbert space, expanding representational dimensionality without requiring deeper layers or additional qubits. The breakthrough delivers a method that jointly learns how to transform and observe the quantum state for faithful image reconstruction, optimising both variational angles and Hermitian parameters. This innovative design exploits the expansive Hilbert space of quantum systems and the representational benefits of quantum entanglement and superposition, potentially unlocking new capabilities in image processing. Experiments revealed that ANO-VQCs can achieve up to five-fold increases in image resolution while maintaining a relatively small model size, indicating a promising avenue for quantum machine learning applications.

The model effectively expands the expressive power of VQCs without necessitating deeper layers or increased qubit counts, jointly optimising both variational angles and Hermitian parameters to learn optimal transformation and observation of quantum states for accurate image reconstruction. Quantitative improvements in metrics such as MSE, PSNR, and SSIM were observed on the MNIST dataset compared to models employing fixed observables, confirming the efficacy of the proposed approach. However, the authors acknowledge a slight increase in LPIPS, suggesting a trade-off between sharpness and perceptual realism, a tunable balance that requires careful consideration. The findings highlight the potential of adaptive measurement design as a resource-efficient mechanism for quantum learning models, offering a pathway towards more compact and powerful quantum image processing techniques. Future research will focus on scaling ANO-VQCs to larger quantum systems, integrating classical-quantum hybrid post-processing, and extending the methodology to more complex datasets and generative vision tasks.