Topological Quantum Computation: From Concepts to Experiments
Prof. Dr. Markus Müller (Department of Physics, Swansea University, Swansea, Wales/UK)

Quantum computers hold the promise to allow one to solve important problems that cannot be efficiently treated on classical computers. To date, the construction of a fault-tolerant quantum computer remains a fundamental scientific and technological challenge, due the influence of unavoidable noise which affects the fragile quantum states. In our talk, we first introduce basic concepts of topological quantum error-correcting codes, which allow one to protect quantum information during storage and processing by distributing logical quantum information over quantum many-body spin systems. We then discuss progress on experimental quantum error correction, in particular the realisation of a minimal topological color code with trapped ions, which for the first time demonstrated basic quantum computations on an encoded qubit. In the second part, I will focus on fault-tolerant quantum computing in trapped-ion quantum processors, in which scalability is achieved by shuttling ions between various trapping regions and by a rich toolbox of ion-crystal reconfiguration techniques. Here, I will present recent theory work of our group on resource-efficient and fault-tolerant protocols to control single and coupled logical qubits of increasing size and robustness.