Description
Quantum computers hold the promise to allow one to solve
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 will first introduce basic concepts of quantum error
correction based on 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 present recent
theory work of our group and experimental progress towards
fault-tolerant quantum error correction and control of
coupled logical qubits of increasing size and robustness in
scalable trapped-ion architectures.
