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Diffusion-based generative models have recently emerged as powerful solutions for high-quality synthesis in multiple domains. Leveraging the bidirectional Markov chains, diffusion probabilistic models generate samples by inferring the…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
Quantum computing offers fundamentally more expressive mechanisms for generative modeling, yet current approaches remain constrained by classical neural components that bottleneck quantum capability and hardware efficiency. We propose the…
Diffusion MRI (dMRI) is an important neuroimaging technique with high acquisition costs. Deep learning approaches have been used to enhance dMRI and predict diffusion biomarkers through undersampled dMRI. To generate more comprehensive raw…
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…
Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to…
Quantum Darwinism (QD) proposes that classical objectivity emerges from the broadcast of information about a microscopic degree of freedom into multiple fractions of a many-body environment. Such a broadcast of information is in sharp…
The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved…
This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…
We study the spreading of a quantum-mechanical wavepacket in a one-dimensional tight-binding model with a noisy potential, and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite…
Quantum generative modeling is a growing area of interest for industry-relevant applications. With the field still in its infancy, there are many competing techniques. This work is an attempt to systematically compare a broad range of these…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through…
Quantum technology has entered the era of noisy intermediate-scale quantum (NISQ) information processing. The technological revolution of machine learning represented by generative models heralds a great prospect of artificial intelligence,…
Generative neural image compression supports data representation at extremely low bitrate, synthesizing details at the client and consistently producing highly realistic images. By leveraging the similarities between quantization error and…
Discrete diffusion models represent a significant advance in generative modeling, demonstrating remarkable success in synthesizing complex, high-quality discrete data. However, to avoid exponential computational costs, they typically rely…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…
We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. Contrary to existing QGM approaches, we perform…
We propose a hybrid protocol to classify quantum noises using supervised classical machine learning models and simple quantum key distribution protocols. We consider the quantum bit error rates (QBERs) generated in QKD schemes under…