Speaker
Description
Introduction
Generative Diffusion Models (GDMs) are an emerging Machine Learning paradigm where data is corrupted with classical noise and then a Neural Network (NN) learns to remove it in order to recover the unknown initial data distribution. We propose three approaches for a quantum generalization of GDMs with different combinations of classical/quantum forward and backward dynamics as in Fig. 1. Here, quantum noise is exploited as a beneficial ingredient to generate complex distributions.
Methods
We train the Classical-Quantum GDM model using a dataset composed of random points distributed along a line segment. The diffusion process is implemented via a classical Markov chain of Gaussian transition kernels. The denoising process is realized via a parameterized quantum circuit trained to estimate mean and covariance of the kernel of a denoising Markov chain. For the Quantum-Classical (QCGDM) and Quantum-Quantum (QQGDM) models, the quantum forward dynamics is initialized with a pure quantum state that is iteratively degraded by depolarizing channels until it is maximally mixed. In QCGDMs the denoising is implemented with NNs trained to simulate a dynamic to obtain an approximation of the initial state. In QQGDMs the backward is realized with a non-unitary quantum dynamic in the context of open quantum systems.
Results
The results of a simulation of a CQGDM is shown in Fig. 2a. The model reconstructs the initial data distribution with a good approximation quantified by the Kullback-Leibler divergence between the original and reconstructed distributions. In Fig. 2b we show the evolution of the loss during the training of the model. In Fig. 2c and 2d we show the simulation on a single-qubit system for ten QCGDMs and QQGDMs, respectively. In Fig. 2e is reported the evolution of the loss during the training of both models.
Discussion
Quantum systems can represent intractable distributions that are classically inefficient to reproduce. At the best of our knowledge, CQGDM and QCGDM are the first implementations of hybrid classical-quantum diffusion models. This work pave the way for new quantum generative diffusion algorithms for real-world applications, and the design and realization of quantum GDMs could alleviate and reduce the computational resources.
