Hitting Times of Quantum Random Walks

Random walks have been applied in a many different fields for a long time. More recently, classical random walks are being used in wide variety of computer algorithms used to solve complex computational problems like 2-SAT, 3-SAT and the estimation of the volume of complex bodies. In this thesis we look into the quantum version of the familiar...

Superconducting diode effect from Josephson junctions

Conventional semiconductor diodes dissipate energy in the form of heat when current passes through them. This is unwanted in, for example, cryogenic environments. Using a superconducting diode could mitigate this problem. These have been made by using special materials or combining multiple different circuit elements. We provide a systematic...

Using a Physics-Informed Neural Network to solve the Ideal Magnetohydrodynamic Equations

In this work we investigate neural networks and subsequently physics-informed neural networks. Physicsinformed neural networks are away to solve physical models that are based on differential equations by using a neural network. The wave equation, Burgers’ equation, Euler’s equation, and the ideal magnetohydrodynamic equations are introduced and...

Reflection Positivity in Heisenberg and Ice-Type Models

This thesis gives a thorough description of the mathematical tool called reflection positivity, which can be used to prove the occurrence of phase transitions in physical models. A major result, although already known, is a theorem that gives tractable conditions on the Hamiltonian such that the Boltzmann functional is reflection positive. In...

Conductance of a nanowire with nonlinear electrostatics

The electrostatics has effect on conductance of nanowire devices. In this model electrostatics are described by nonlinear coupling of the Poisson and the Schr¨odinger equations. In presence of magnetic and electric field and spin-orbit interaction, conductance develops a feature called the helical gap. This gap is characterised by a drop of...

The Kernel Polynomial Method applied to tight binding systems with time-dependence

The Kernel Polynomial Method (KPM) is a method to approximate any function as a polynomial of finite order. In this research the KPM will be used to approximate the density of states and expectation values of physical observables in a tight binding system. To be able to use the KPM a tight binding Hamiltonian is obtained by using the python...

Pulse optimization for multi-qubit gates in transmon system

In transmon qubits, the leading source of errors for quantum gates is the existence of higher energy levels, besides the |0> and |1> states which form the computational subspace. Several methods have been developed to eliminate these errors systematically by clever use of the available experimental controls. In this bachelor thesis we focus on...

Iterative Methods for Solving the Schrödinger Equation on a Rectangular Scattering Region

Four iterative methods were used to solve the schrödinger equation on a rectangular scattering region with a uniform potential, namely GMRES, restarted GMRES, BiCGStab and IDR(s). A preconditioner like a shifted-Laplacian is tried to improve the convergence behaviour of GMRES. Finally, a disorded potential is introduced in the form of a random...