Quantum computation is one of the most fundamental and important research topics today, from both theoretical and experimental perspectives. A fault tolerant computation scheme, such as that protected against dephasing or decay of quantum information, is crucial for this purpose. It has been known for some time that a class of quasi-particles of non-abelian braiding statistics, such as the Majorana fermions, can be an excellent platform to achieve such a topologically protected quantum computation. While recent discovery of the Majorana fermions in semiconductor nanowires have boosted the quantum computation community, other material platforms, in particular graphene, are also being researched extensively. Much research is directed towards electron-electron interaction and non-trivial p-type superconductivity in graphene with the ultimate aim to create and detect Majorana fermions in these systems. This Discussion Meeting on “Advances in Graphene, Majorana fermions, and Quantum Computation” showcases in-depth scientific presentations and debates on these globally active fields of research today. The participation of many leaders in these fields from all over the world will make this meeting a scientifically exciting event for the local active research community.