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 Quantum computing, based on different principles than classical computing, has raised high expectations regarding the increase of computational speed in nano-sized quantum systems. Therefore, the search for implementations of quantum logic gates in photons, spin states, atom/ion traps or superconducting materials, for example, is a very active research area. Graphene has demonstrated already the possibility of implementing reversible logic gates, therefore becoming a compelling candidate for quantum computing applications. The paper presents several proposals of quantum logic gates implementation in graphene, which could work at room temperature and require only current measurements as readout procedures; examples of such quantum gates are Hadamard, C-NOT, C-phase and Toffoli gates. Besides these gates, it is shown that quantum algorithms, such as the modified Deutsch-Jozsa algorithm, can be implemented also in graphene.

Besides the plenty of applications of graphene allotropes in condensed matter and nanotechnology, we argue that graphene sheets might be engineered to support room-temperature topological quantum processing of information. The argument is based on the possibility of modeling the monolayer graphene effective action by means of a 3d Topological Quantum Field Theory of BF-type able to sustain non-Abelian anyon dynamics. This feature is the basic requirement of recently proposed theoretical frameworks for fault-tolerant and decoherence protected quantum computation.