With the help of quantum mechanics, digital quantum hardware may be able to tackle some of the problems that are too difficult for ordinary computers. But despite these expectations and the ongoing... Show moreWith the help of quantum mechanics, digital quantum hardware may be able to tackle some of the problems that are too difficult for ordinary computers. But despite these expectations and the ongoing effort of the research community, reliable quantum computers are not yet realized in a lab setting. The optimal strategies for early applications of such special hardware are not settled either. The present thesis addresses these issues of implementing and harnessing quantum computers.Firstly, several strategies are introduced to implement and characterize digital quantum hardware using the technique called braiding. Two realizations are considered: the edge modes of topological superconductors and the parafermionic modes in Fractional Quantum Hall materials.Secondly, this work explores applying quantum computers to prepare simulated ground states (lowest-energy configurations) of complex quantum systems. To this end, several new techniques are presented in the context of variational quantum algorithms, simulated cooling, and quantum control theory. Show less
Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they... Show moreMajorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with equal probability. Building on a recent proposal to inject edge vortices in a chiral mode by means of a Josephson junction, we show how the fusion rule manifests itself in an electrical measurement. A 2π2π phase shift at a pair of Josephson junctions creates a topological qubit in a state of even-even fermion parity, which is transformed by the chiral motion of the edge vortices into an equal-weight superposition of even-even and odd-odd fermion parity. Fusion of the edge vortices at a second pair of Josephson junctions results in a correlated charge transfer of zero or one electron per cycle, such that the current at each junction exhibits shot noise, but the difference of the currents is nearly noiseless. Show less
Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they... Show moreMajorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with equal probability. Building on a recent proposal to inject edge vortices in a chiral mode by means of a Josephson junction, we show how the fusion rule manifests itself in an electrical measurement. A 2π2π phase shift at a pair of Josephson junctions creates a topological qubit in a state of even-even fermion parity, which is transformed by the chiral motion of the edge vortices into an equal-weight superposition of even-even and odd-odd fermion parity. Fusion of the edge vortices at a second pair of Josephson junctions results in a correlated charge transfer of zero or one electron per cycle, such that the current at each junction exhibits shot noise, but the difference of the currents is nearly noiseless. Show less
Carmi, A.; Herasymenko, Y.; Cohen, E.; Snizhko, K. 2019
