Quantum walks on graphene nanoribbons using quantum gates as coins

Both discrete and continuous quantum walks on graphs are universal for quantum computation. We define and use discrete quantum walks on the graphene honeycomb lattice to investigate the possibility of using graphene armchair and zigzag nanoribbons to implement quantum gates. The probability distribution of the quantum walker location represents the particle (electron) density distribution on the graphene lattice. We use a universal set of quantum gates as coins that drive the quantum walk and show that different quantum gates result in distinguishable particle distributions on the graphene lattice.