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... Show moreQuantum 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. 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. 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. Show less
Thermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems... Show moreThermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems by examining the bulk behavior of their constituents, it is anchored in the statistical equivalence of equilibrium configurations of a formally infinite number of microscopic constituents. A question of its validity arises when one scales down to small quantum systems. Here, we have derived dynamic non-equilibrium relations that surprisingly resemble the classical thermodynamics laws, with a mix of quantum features that encode the dynamics of quantum information. Understanding the relation between the out-of-equilibrium dynamics of finite-size quantum systems and their initial thermodynamic state might have been a purely academic exercise fifteen years ago. But now, thanks to ultra-cold atomic quantum simulators and progress in quantum computers, the thermodynamics of finite-size quantum systems has practical implications too. The findings of this thesis contribute to understanding quantum many-body systems, particularly in the context of entanglement, non-equilibrium dynamics, thermalization, and charge transport. Show less
Optical cavities are useful tools to enhance the interaction between light and matter, which is important to make good quantum emitters. However, it turns out that the cavities themselves (without... Show moreOptical cavities are useful tools to enhance the interaction between light and matter, which is important to make good quantum emitters. However, it turns out that the cavities themselves (without any quantum emitters) are already interesting objects to study. When these cavities become very small, non-paraxial effects become important to describe the eigenmodes of the cavity. This thesis describes both the theoretical predictions of the cavity and shows the corresponding experiments. Show less
Biological cells, the basic building blocks of all life forms, are surrounded by a lipid membrane. More than half of the membrane is occupied by membrane proteins, which can regulate the cell... Show moreBiological cells, the basic building blocks of all life forms, are surrounded by a lipid membrane. More than half of the membrane is occupied by membrane proteins, which can regulate the cell functionality through specific arrangements. To regulate the arrangements several proteins have to work together. In addition to direct forces, there exists an indirect force between the proteins, which stems from their deformation of the membrane and contributes to their self-organization. Since the actual membrane is very crowded and proteins are too tiny and complex to measure this interaction, in this thesis we used a model system consisting of lipid membranes and solid particles to study the deformation-mediated interaction. We experimentally confirmed for the first time that, unlike many known forces, this deformation-mediated interaction is not additive, i.e. the strength and range of three (or more) deformations cannot be obtained by simple addition of the interactions between pairs of deformations. We found that the interaction weakens with increasing number of membrane-deforming particles and that the particle become less ordered. We investigated deformations in both directions of the membrane and found that the interaction can be both repulsive and attractive, and furthermore depends on the shape of the deformation. This thesis helps to better understand the organization of proteins that deform cellular membranes. Show less
