  The rise of graphene opens a new door to qubit implementation, as discussed
in the recent proposal of valley pair qubits in double quantum dots of gapped
graphene (Wu et al., arXiv: 1104.0443 [cond-mat.mes-hall]). The work here
presents the comprehensive theory underlying the proposal. It discusses the
interaction of electrons with external magnetic and electric fields in such
structures. Specifically, it examines a strong, unique mechanism, i.e., the
analogue of the 1st-order relativistic effect in gapped graphene. This
mechanism is state mixing free and allows, together with the electrically
tunable exchange coupling, a fast, all-electric manipulation of qubits via
electric gates, in the time scale of ns. The work also looks into the issue of
fault tolerance in a typical case, yielding at 10oK a long qubit coherence time
(~O(ms)).
