We propose to create high fidelity quantum gates using qubits encoded in the hyperfine states of 43Ca+ trapped in a linear Paul trap. The use of magnetic field insensitive (m=0) states drastically decreases decoherence due to stray magnetic fields. We will investigate a number of entangling gates and set up simple error correction schemes. In particular, we plan to implement a number of quantum gates that rely on collective laser excitation of the ions. For this 43Ca+ offers the opportunity to use the narrow line width S-D quadrupole transition. This will make it possible to implement the collective laser excitation gate using magnetic field insensitive states, while greatly reducing decoherence due to spontaneous decay. These new types of quantum gates will be studied in this project in addition to quantum gate operations relying on Raman interactions mediated by a dipole transition. We expect the proposed research will provide an important step towards more demanding quantum computation. The fellowship will help to strengthen QIP research in the European Union while supplying ample opportunity for career development for the fellow.