Limitations and Opportunities of Noisy Quantum Devices

In this work, we first analyse a theoretical technique based on entropic inequalities, which in principle can be used to compare classical and quantum algorithms running on noisy quantum devices. The technique has been used in the past for depolarizing noise, and has shown that for NISQ variational quantum algorithms (VQAs) to give an advantage...

Classical and Quantum Simulation of Stoquastic Hamiltonian Systems

Quantum systems are in general not e_ciently simulatable by classical means. If one wishes to determine (some of) the eigenvalues of a Hamiltonian H that is associated with a quantum system, there are two favoured strategies: Quantum simulation and quantum Monte Carlo schemes. The former strategy uses an experimentally well-controllable quantum...

Inequalities and Quantum Entanglement: From the Cauchy-Schwarz Inequality to Non-linear Entanglement Witnesses

In this thesis, two topics are studied: mathematical inequalities and non-linear quantum entanglement witnesses. First, various inequalities, like the Cauchy-Schwarz inequality (on finite dimensional vector spaces) and Jensen's inequality, along with their extensions and generalisations, are proved and discussed. The intimate relationship...