October 2023

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Quantum-Enhanced Denoising DiffusionModels

Quantum-Enhanced Denoising Diffusion Models

Abstract:

Machine learning models for generating images have gained much notoriety in the past year. DALL-E, Craiyon and Stable Diffusion can generate high-resolution images, by users simply typing a short description (prompt) of the desired image. Another growing field is quantum computing, particularly quantum-enhanced machine learning. Quantum computers solve problems using their unique quantum mechanical properties. In this paper we investigate how the use of Quantum-enhanced Machine Learning and Variational Quantum Circuits can improve image generation by diffusion-based models. The two major weaknesses of classical diffusion models are addressed, the low sampling speed
and the high number of required parameters. Implementations of a quantum-enhanced denoising diffusion model will be presented, and their performance is compared with that of classical models, by training the models on well-known datasets (MNIST digits and fashion, CIFAR10). We show, that our models deliver better performance (measured in FID, SSIM and PSNR) than the classical models with comparable number of parameters.

Author:

Gerhard Stenzel

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Jonas Stein, Andreas Sedlmeier

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Dimensionality Reduction with Autoencodersfor Efficient Classification with VariationalQuantum Circuits

Dimensionality Reduction with Autoencoders for Efficient Classification with Variational Quantum Circuits

Abstract:

Quantum computing promises performance advantages, especially for data-intensive and complex computations. However, we are currently in the Noisy Intermediate-Scale Quantum era with a limited number of qubits available, which makes it challenging to realize these potential quantum advantages in machine learning. Several solutions, like hybrid transfer learning have been proposed, whereby a pre-trained classical neural network acts as the feature extractor and a variational quantum circuit as the classifier. While these approaches often yield good performance, it is not possible to clearly determine the contribution of the classical and quantum part. The goal of this thesis is therefore to introduce a hybrid model that addresses these limitations and implements a clear distinction between the classical and quantum parts. An autoencoder is used to reduce the input dimension. We compare the performance of transfer learning models (Dressed Quantum Circuit and SEQUENT) and a variational quantum circuit with amplitude embedding against our model. Additionally, the performance of a purely classical neural network on the uncompressed input and an autoencoder in combination with a neural network will be examined. We compare the test accuracies of the models over the datasets Banknote
Authentication, Breast Cancer Wisconsin, MNIST and AudioMNIST. The results show that the classical neural networks and the hybrid transfer learning approaches perform better than our model, which matches our expectations that the classical part in transfer learning plays the major role in the overall performance. Compared to a variational quantum circuit with amplitude embedding, no significant dierence can be observed, so that our model is a reasonable alternative to this.

Author:

Jonas Maurer

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Philipp Altmann, Leo Sünkel

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Approximating Quadratic Unconstrained Binary Optimization Problems using Graph Convolutional Neural Networks

Approximating Quadratic Unconstrained Binary Optimization Problems using Graph Convolutional Neural Networks

Abstract:

The quantum annealing hardware currently available has not yet reached the stage to successfully compete with ecient heuristics on classical machines, due to limitations in size and connectivity. Confronted with this challenge, the approach to approximate QUBO matrices by removing certain entries before solving them on the quantum hardware has been introduced. This is done to reduce the size and the complexity of the embedding, anticipating benefits with regard to the size of the solvable problems as well as the quality of the solutions.
We will extend this approach by using artificial neural networks to generate suitable approximations based on the structure of the matrix. The proposed model consists of two separate networks, a graph convolutional neural network to compute features for the nodes in the QUBO graph and a second fully connected network to derive a decision, whether the connection between two nodes should be removed from the matrix. A genetic algorithm was employed to train the model, using instances of seven dierent problems. Problem specific phase transitions were taken into account to confront the model with
easy and hard problem instances.
The trained models were subsequently evaluated using classical and quantum solvers, comparing the performance of the approximated matrix with the original matrix, another approximation strategy and classical approaches. The experiments provided satisfying results for certain problems, as the approximated matrices were partially able to produce even better results than the original matrices. In other respects, it became apparent, that this approach is not applicable to all problems.

Author:

Felix Ferdinand Mindt

Advisors:

Claudia Linnhoff-Popien, David Bucher, Sebastian Zielinski

Student Thesis | Published October 2023 | Copyright © QAR-Lab
Direct Inquiries to this work to the Advisors