Enhancing Quantum Diffusion Models for Complex Image Generation

TL;DR

This paper tackles the challenge of scalable, high-fidelity multi-class image generation on NISQ devices by introducing a Hybrid Quantum-Classical U-Net that routes a classical encoder’s latent representation through a quantum bottleneck governed by a parameterized quantum circuit. A core innovation is Adaptive Non-Local Observables (ANO), which learn a set of trainable Hermitian measurements to extract rich, non-local features from entangled quantum states, coupled with a 1D cluster-state-like mixing layer to enable global information propagation. The architecture is evaluated on the full MNIST dataset (digits 0–9), showing stable reverse diffusion dynamics and the ability to generate distinct, recognizable digits across all classes, addressing mode collapse observed in earlier quantum baselines. The results suggest a practical pathway for quantum-assisted diffusion in the NISQ era, guiding design choices for quantum bottlenecks, feature extraction, and skip connections to preserve semantic structure during generation.

Abstract

Quantum generative models offer a novel approach to exploring high-dimensional Hilbert spaces but face significant challenges in scalability and expressibility when applied to multi-modal distributions. In this study, we explore a Hybrid Quantum-Classical U-Net architecture integrated with Adaptive Non-Local Observables (ANO) as a potential solution to these hurdles. By compressing classical data into a dense quantum latent space and utilizing trainable observables, our model aims to extract non-local features that complement classical processing. We also investigate the role of Skip Connections in preserving semantic information during the reverse diffusion process. Experimental results on the full MNIST dataset (digits 0-9) demonstrate that the proposed architecture is capable of generating structurally coherent and recognizable images for all digit classes. While hardware constraints still impose limitations on resolution, our findings suggest that hybrid architectures with adaptive measurements provide a feasible pathway for mitigating mode collapse and enhancing generative capabilities in the NISQ era.

Figures (6)

• Figure 1: The parameterized quantum circuit used in our Quantum Bottleneck. This structure implements the optimal decomposition for arbitrary two-qubit entangling gates, characterized by the parameters $\alpha, \beta, \gamma$. Note the alternating CNOT direction and the specific rotation angles derived from the canonical decomposition.
• Figure 2: Schematic of the Quantum Bottleneck with Adaptive Non-Local Observables (ANO). Unlike standard VQCs that output $N$ local measurements, our ANO framework employs a set of $K$ trainable Hermitian operators $\{H_k(\phi_k)\}$. This allows the extraction of high-dimensional feature vectors ($K \ge N$) from the entangled quantum state $|\psi(\theta)\rangle$, effectively acting as a learnable quantum lens for super-resolution tasks.
• Figure 3: Visualization of the single-qubit reduced state distribution on the Bloch sphere generated by our ANO-based ansatz. Each red point represents the state of the first qubit traced out from the multi-qubit system, sampled over random circuit parameters. (Left) Points distributed strictly on the surface indicate product states with no entanglement. (Right) Points filling the interior volume demonstrate the generation of strong multi-partite entanglement, as the reduced state becomes mixed due to correlations with other qubits. This volumetric coverage visually corroborates the high Meyer-Wallach measure and Expressibility scores.
• Figure 4: Schematic of the Hybrid Quantum-Classical U-Net Architecture. The model integrates a quantum bottleneck for feature extraction and employs a skip connection to preserve original semantic information during the reverse diffusion process.
• Figure 5: Dynamics of Reverse Diffusion. The columns represent discrete time steps from pure noise (Step 0) to the final generated sample (Step 10). The rows correspond to different digit classes. The model successfully reconstructs the global topology of each digit, demonstrating stable reverse dynamics typically difficult to achieve in NISQ-era quantum models.