Spin qubits in graphene quantum dots

The electron spin is a very promising candidate for a solid-state qubit [1]. Major experimental breakthroughs have been achieved in recent years using quantum dots formed in semiconductor heterostructures based on GaAs technology [2, 3, 4, 5]. In such devices, the major sources of spin decoherence have been identified as the spin-orbit interaction, coupling the spin to lattice vibrations [6, 7, 8], and the hyperfine interaction of the electron spin with the surrounding nuclear spins [9, 10, 11, 12, 13, 14]. Therefore, it is desirable to form qubits in quantum dots based on other materials, where spin-orbit coupling and hyperfine interaction are considerably weaker [15]. It is well known that carbon-based materials such as nanotubes or graphene are excellent candidates. This is so because spinorbit coupling is weak in carbon due to its relatively low atomic weight, and because natural carbon consists predominantly of the zero-spin isotope 12C, for which the hyperfine interaction is absent. Here we show how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy is lifted. We show that this problem can be avoided in quantum dots with so-called armchair boundaries. We furthermore show that spin qubits in graphene can not only be coupled (via Heisenberg exchange) between nearest neighbor quantum dots but also over long distances. This remarkable feature is a direct consequence of the Klein paradox being a distinct property of the quasirelativistic spectrum of graphene. Therefore, the proposed system is ideal for fault-tolerant quantum computation, and thus for scalability, since it offers a low error rate due to weak decoherence, in combination with a high error threshold due to the possibility of long-range coupling.