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

TL;DR

This work uses the formalism of quantum stochastic walks to show that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fr\'echet Inception Distance than using totally classical dynamics.

Abstract

Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.

Figures (9)

• Figure 1: Example of dm for discrete data. An initial data distribution $q(\mathbf{x}_0)$ is transformed into a uniform categorical distribution $\pi(\mathbf{x}_2)$ after $T=2$ time steps. The forward transition kernel is $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})$, while $p(\mathbf{x}_{t-1}|\mathbf{x}_{t})$ is the transition kernel of the backward process obtained by training an ann.
• Figure 2: The kl divergence between the populations of a single qsw and the uniform distribution on a cycle graph of $8$ nodes for different value of $\omega$ after $T = 20$ time steps. The walker is initially in the node $0$, corresponding to the state $\rho = \ketbra{0}{0}$, and its evolution over the graph is obtained by solving the equation \ref{['eq:qsw']}.
• Figure 3: Illustration of the model. Each pixel of an image sample represents an independent quantum stochastic walker moving on a cycle graph of $8$ nodes that correspond to the gray intensity values. The walker moves on the graph by \ref{['eq:qsw']}.
• Figure 4: The box plot of fid value for different value of $\omega$. Every box plot is obtained from $10$ different repetitions of for the same value of $\omega$ with $T=20$, $8$-cycle graph. Mean and standard error of the mean are also reported. The plot show how the hybrid quantum-classical diffusion dynamics $(\omega = 0.3)$ results to generate statistically better image datasets.
• Figure 5: Image generation with qsw-based dm via a quantum ($\omega =0$), hybrid $(\omega = 0.3)$ and a classical ($\omega =1$) forward chain of $T=20$ time steps. We use the models with the inferior median values of fid between the 10 repetitions of \ref{['fig:Fidboxplot']}. We report the first two steps of the forward chain (in the first row) of 9 different samples, and the evolution of the distribution of the pixel values for the entire dataset of digits $0$ of MNIST (blue bins in the second row) that is compared with the final uniform prior (orange bins in the second row). The kl divergence value between the two distributions is reported on the top. We also illustrate the final two steps of 9 generated samples, and the fid score between the entire training dataset and generated dataset is reported (third row). In the last row, we compare the distribution of the pixel values of the entire generated dataset (blue) with the training dataset distribution (orange), and kl divergence between them.