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
This thesis is a collection of theoretical works aiming at adjusting quantum algorithms to the hardware of quantum computers. The overarching topic of these efforts is to enable digital quantum... Show moreThis thesis is a collection of theoretical works aiming at adjusting quantum algorithms to the hardware of quantum computers. The overarching topic of these efforts is to enable digital quantum simulation, the process of approximating the ground state of an arbitrary physical system with elementary operations of a quantum computer. For fermionic systems, a class including molecules and materials, the impact of quantum computing would be undoubtedly high, and algorithms exist for their simulation. However, there is a certain gap between the requirements of those algorithms and what actual quantum devices can provide: it seems that our expectations of a fully-fledged quantum computer still exceed our capabilities to build it. To make quantum simulation feasible, we seek to adapt quantum algorithms to three different types of device limitations within this thesis. Show less
