⚛️ quantum physics

Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion

This paper proposes and implements two physics-inspired protocols for Quantum Diffusion Models that leverage quantum stochastic walks and intrinsic noise from real IBM quantum hardware to generate MNIST images with improved performance, demonstrating that quantum noise can be exploited as a useful resource rather than a limitation in near-term quantum generative AI.

Original authors: Marco Parigi, Stefano Martina, Francesco Aldo Venturelli, Filippo Caruso

Published 2026-10-12

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Marco Parigi, Stefano Martina, Francesco Aldo Venturelli, Filippo Caruso

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the rapidly evolving world of artificial intelligence, a specific type of computer program has emerged that excels at creating new, original content. These systems, known as generative models, learn the hidden patterns within a collection of existing data—such as thousands of photographs—and then use that knowledge to invent fresh images that look just as real. One of the most powerful methods for doing this is called a diffusion model. Imagine a process where a clear image is slowly, step-by-step, turned into static noise, like television snow. A diffusion model learns to reverse this process. It is trained to take a screen full of random noise and gradually peel away the chaos, step by step, until a coherent picture emerges. This technique has become a cornerstone of modern creative technology, capable of producing stunning visuals and sounds.

At the same time, scientists are exploring a different kind of computing power based on the strange rules of quantum mechanics. Unlike the computers we use every day, which process information as simple on or off switches, quantum computers use particles that can exist in multiple states at once. This allows them to solve certain complex problems in ways that classical machines cannot. However, current quantum computers are still in their early stages. They are small, fragile, and prone to errors caused by a phenomenon known as quantum noise. This noise usually disrupts calculations, forcing researchers to spend immense resources trying to fix or hide it. The question driving a new line of research is whether these noisy machines can do something useful despite their flaws, or if they must wait until they are perfect to be of any value.

A team of researchers from the University of Florence and other institutions has taken a bold step in answering this question. Instead of trying to eliminate the noise in their quantum computer, they decided to use it as a tool. They developed a new way to build an image-generating AI that runs directly on a real, imperfect quantum processor. Their work suggests that the very noise that usually breaks quantum calculations can actually help a generative model create better images than a purely classical approach. By treating the quantum noise not as a bug, but as a feature, they demonstrated a path forward for artificial intelligence that works with the hardware we have today, rather than waiting for the hardware of tomorrow.

The researchers began by studying how information moves through a network. In their model, they treated each pixel of an image as a traveler moving across a map. In a standard computer, this traveler moves randomly, like a person flipping a coin to decide which street to take next. This is a slow, diffusive process. In a quantum system, however, the traveler can exist in many places at once, moving through the map in a wave-like pattern that spreads much faster. The team created a hybrid system where the traveler's movement is a mix of both the slow, random steps of a classical computer and the fast, wave-like spread of a quantum computer. They found that when they balanced these two behaviors just right, the system explored the possibilities of the image more efficiently.

To test this, they focused on generating images of handwritten digits, a standard test for artificial intelligence. They replaced the random noise injection step of the standard AI process with their new quantum-inspired method. In the first part of their study, they simulated this process on powerful classical computers to see how different mixes of quantum and classical behavior would perform. They discovered that a specific blend, where the quantum effects were present but not overwhelming, produced the best results. The images generated by this hybrid method were statistically closer to the real training data than those produced by a purely classical method. The system was also more consistent, producing high-quality results more reliably across many different attempts.

Encouraged by these simulations, the team moved to the next phase: running the experiment on actual hardware. They used a real quantum processor from IBM, a machine that currently contains only a few hundred qubits, the basic units of quantum information. This specific machine is known to be noisy, meaning its calculations are often disturbed by the environment. The researchers designed a circuit that used just four qubits to generate images. They mapped the different shades of gray in a pixel to the positions on a small loop, or cycle, of eight points. The quantum computer then ran a process where the "walker" moved around this loop, with the machine's natural noise helping to scramble the data in a controlled way.

The results were striking. Even with the limitations of the current hardware, the quantum computer successfully generated images of handwritten digits. While the images were not perfect, the experiment proved that a quantum device could be used to drive the forward part of a generative model. The researchers found that the noise inherent in the machine helped corrupt the data in a way that the AI could later learn to reverse. This is a significant departure from the usual approach in quantum computing, where scientists spend years trying to suppress noise to get a clean signal. Here, the noise was the engine of the process.

The study also highlighted the practical advantages of this approach. Because the quantum part of the model only needed to handle the intensity levels of a single pixel, the number of qubits required did not grow with the size of the image. They were able to generate full 28-by-28 pixel images using only four qubits. This scalability suggests that even small, noisy quantum computers could eventually contribute to generating much larger and more complex images. The team noted that while the images generated by the real hardware were slightly less sharp than those from their simulations, the difference was understandable given the physical constraints of the machine.

Ultimately, this work offers a new perspective on the future of quantum artificial intelligence. It challenges the idea that quantum computers must be perfect before they can be useful. By showing that the noise of a real quantum device can be harnessed to improve the quality of generated data, the researchers have opened a door to a new kind of hybrid computing. Their findings suggest that in the near future, we may not need to wait for error-free quantum machines to see the benefits of quantum AI. Instead, we can start building systems today that embrace the imperfect, noisy nature of the technology to create something new and useful. The path forward involves refining these methods, perhaps by better understanding the specific types of noise in different machines, but the core idea—that noise can be a resource rather than a barrier—has been demonstrated.

Technical Summary: Physics-Inspired Generative AI Models via Real Hardware-Based Noisy Quantum Diffusion

Problem Statement
Quantum Diffusion Models (QDMs) represent a promising paradigm for enhancing Generative AI by leveraging quantum properties. However, existing QDM algorithms face significant scalability challenges on current Noisy Intermediate-Scale Quantum (NISQ) devices. Traditional approaches often rely on simplified scenarios, pre-processing techniques, or classical latent models to reduce dimensionality. Furthermore, quantum noise is typically viewed as a detrimental factor requiring mitigation or correction, which demands a high overhead of physical qubits. The authors address the challenge of developing scalable QDM protocols that function effectively on near-term hardware, specifically exploring whether quantum noise can be utilized as a resource rather than a hindrance.

Methodology
The paper proposes and implements two distinct physics-inspired protocols for image generation, utilizing the formalism of Quantum Stochastic Walks (QSWs) and Discrete-Time Quantum Walks (DTQWs).

Hybrid Quantum-Classical Stochastic Diffusion (Simulation):
- The authors replace the classical stochastic dynamics in the forward diffusion process of a Diffusion Model (DM) with QSW dynamics.
- Formalism: They employ the Kossakowski–Lindblad-Gorini master equation to describe the evolution of a quantum stochastic walker on a graph. A control parameter, $\omega \in [0, 1]$ , tunes the interplay between coherent quantum evolution ( $\omega=0$ ) and incoherent classical dynamics ( $\omega=1$ ).
- Setup: Each pixel of an image is treated as an independent quantum stochastic walker evolving on a cycle graph of 8 nodes (representing grayscale levels 0–7).
- Backward Process: The denoising (backward) process is implemented classically using a Multi-Layer Perceptron (MLP) trained to reverse the forward trajectory.
- Evaluation: The performance is evaluated using the Fréchet Inception Distance (FID) on the MNIST dataset, comparing pure quantum, pure classical, and hybrid ( $\omega \in (0,1)$ ) forward dynamics.
Real Hardware Implementation on NISQ Devices:
- The authors implement a DTQW on a real IBM quantum processor (ibm_brisbane) to generate images.
- Circuit Design: The algorithm utilizes a quantum circuit with only 4 qubits: 3 qubits for the position of the walker on the 8-node cycle graph and 1 qubit for the "coin" degree of freedom.
- Noise Exploitation: Instead of error correction, the intrinsic noise of the hardware is exploited. The noise level is modulated via delay operations in the circuit, scaled according to a cosine schedule analogous to classical DMs.
- Scalability: Due to the rotation-invariant property of the cycle graph, the forward process is run once for all walkers (pixels) starting from the same initial state, with outcomes remapped to specific pixel values. This allows the generation of $28 \times 28$ images using a fixed number of qubits independent of image dimensions.

Key Contributions

Demonstration of Hybrid Advantage: The study shows that a specific interplay of quantum and classical dynamics in the forward process (specifically at $\omega \approx 0.3$ ) yields statistically more robust models with lower FID scores compared to purely classical dynamics.
Noise as a Resource: The work provides a proof-of-concept for generating images using the intrinsic noise of real NISQ hardware without error correction, framing noise as a useful resource for diffusion.
Resource Efficiency: The proposed QW-based algorithm achieves image generation with a minimal qubit count (4 qubits for $28 \times 28$ images), addressing the scalability limitations of previous QDM approaches that often require dimensionality reduction or large latent spaces.
Empirical Validation: The paper presents results from both simulations (using QuTiP and Qiskit simulators) and execution on the real ibm_brisbane quantum processor.

Results

Simulation Results: In the hybrid scenario with $\omega = 0.3$ , the mean FID value was lower than in the classical case ( $\omega = 1$ ). The box plots indicated that the hybrid model produced FID values more tightly clustered around the median, suggesting greater statistical robustness. The authors attribute this to a balance between quantum coherence and stochastic noise enabling more efficient information transport across the graph.
Hardware Results: The model was trained on 6,903 images of the digit '0' from MNIST. The real hardware implementation achieved an FID of 169, compared to 114 for the hybrid QSW simulation and 200 for the classical simulation.
Comparison: While the real hardware results showed higher FID values than the simulated hybrid model, the authors note that the discrete-time nature of the circuit-based QW implementation (versus the continuous-time QSW simulation) may contribute to differences in noise introduction and convergence.

Significance and Claims
The paper claims to pave the way for new scenarios in large-scale Quantum Generative AI (QGenAI) where quantum noise is neither mitigated nor corrected but is instead exploited as a functional component of the generative process. The authors posit that their hybrid strategy allows for the utilization of existing noisy quantum processors while potentially avoiding common pitfalls of quantum learning models, such as barren plateaus and trainability issues.

The work suggests that the specific balance of quantum and classical dynamics observed in the simulations aligns with previous findings on information transport efficiency in QSWs. The authors conclude that their approach offers a scalable path for QGenAI, particularly for learning unknown quantum phenomena in fields like sensing, metrology, chemistry, and biology, where direct quantum data processing without embedding is desirable. They also note that the methodology has been further developed in collaboration with other groups for medical imaging datasets.

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