The power of one qubit in quantum simulation algorithms

Abstract
This thesis focuses on developing new quantum algorithms, targeting some of the key challenges in the simulation of complex quantum systems.The techniques introduced in this thesis span from quantum state preparation to mitigation of hardware and algorithmic noise, from efficient expectation value measurement to noise-resilient applications in quantum chemistry. 
Quantum computing is an emerging technology, which holds the potential to simulate complex quantum systems beyond the reach of classical numerical methods.Despite recent formidable advancements in quantum hardware, constructing a quantum computer capable of performing useful calculations remains challenging.In the absence of a reliable quantum computer, the study of potential applications relies on mathematical methods, ingenious approximations, and heuristics derived from the fields of application.
A common thread connecting all these algorithms is the introduction of a single auxiliary qubit – a fundamental unit of quantum information – which has an active and distinctive role in the task at hand.

Turning through disorder: Models of bundled mucus strands and microswimmers

Abstract
With every breath you take, you can inhale dangerous particles. The respiratory system relies on mucociliary transport (MCT) to clear the airways of such particles. This works as follows: deposited particles are captured by a mucus layer lining the airways, and this mucus layer is propelled out of the lungs by the beating action of ciliated cells that collectively create a flow. Mucus consists of mucins which give the suspension elastic properties. In this thesis, we focus on a specific structure, bundled mucus strands, present in the upper airways of large mammals. These strands are created in submucosal glands and can be millimetric in length. Once they are released from the glands, they come together to form large networks, that catch large particles and drag these out of the airways. We devised minimal models by which we could numerically investigate how bundled strands contribute to MCT. Specifically, we were interested in how such strands reorient from an orientation parallel to the direction of the flow, when they just emerge from the gland, to a perpendicular orientation. We studied the role of surface interactions, involving another mucin structure, and local inhomogeneities in the fluid flow. We found that both can drive reorientation, but that surface interactions best fit the experimental observations. We also considered a simple model for a microswimmer in a (model) viscoelastic environment, to see how the motion of such a particle is affected by its surroundings. In connecting to experiments, we found that local contact dynamics are key in capturing its reorientation.

Studies of generalized transverse momentum dependent gluon distributions in diffractive processes

Abstract
Hadrons, such as protons and neutrons, constitute the dominant components of the visible matter around us. Understanding their internal structures, consisting of quarks and gluons, collectively referred to as partons, requires high energy hadron collisions to probe their contents. At high energies, where hadrons essentially move at high velocities, gluons are predominantly produced, rendering quark contributions negligible. The gluon distributions are described by parton distribution functions (PDFs) dependent on variables related to the parton and hadron momentum. Including more variables in these functions offers a more complete description of the partons. The six dimensional Generalized Transverse Momentum Distribution PDFs (GTMDs), as the counterpart of the Wigner “mother distribution”, provide a comprehensive depiction of parton distribution inside hadrons. We constructed a generic gluon GTMD model based on established models that have successfully described existing data and introduced a few parameters to fit the data. Our model adequately describes diffractive dijet and J/ψ production data, although some tension remains if one aims for a simultaneous description. Future data from experiments on both existing and new accelerators being built can help clarify this tension.