The recent experimental discovery of graphene [1, 2], filling the gap between quasi 1-dimensional (1-D) nanotubes and 3-D graphite makes truly 2-D solid state systems accessible. Both graphene and carbon nanotubes exhibit unique electronic properties which make these materials promising candidates for future high mobility nanoelectronics and potential extensions to downscaling state-of-the-art silicon technology [3]. In this context, graphene and carbon nanotubes are both interesting materials for future information technology, including solid state quantum computation [4], whose backbone is the initialization, manipulation, and detection of states in two-level quantum systems, the so-called qubits. In semiconductor quantum dots, the electron spin (state up or down) is recognized as a "natural" qubit system [5]. The key ingredients for future quantum applications are long spin lifetimes (T1) and spin-dephasing times (T2) compared to the time constants for manipulating qubits coherently, opening the possibility to couple spin-qubit states. It is interesting to compare nanotubes with graphene from a quantum applications perspective with conventional semiconductor materials.

Although graphene is, from a technological point of view, less mature than nanotubes, significant progress has been made in recent years and a number of groups have reported transport through etched graphene nanoribbons [6-9]. Building on such work, the first graphene quantum dots have been recently fabricated as 0-D building blocks for graphene nanostructures [8, 9]. A remarkable step towards ultra-clean edges for better controlled graphene nanoribbons has been reported very recently [10], using a chemical approach which might open the door to much cleaner graphene devices.

In contrast, carbon nanotube quantum dots have been extensively studied [11] revealing four-fold shell structure that corresponds to the two-fold spin and two-fold orbital degeneracies of the electronic single-particle wave functions. At first glance, nanotubes seem to be more promising than graphene since it is quite obvious that the formation of a 0-D carbon system becomes easier and more controllable when departing from a "natural" 1-D (nanotube) system rather than a 2-D (graphene) system. However, the crystal structure of nanotubes and ideal graphene nanoribbons have many similarities, and a quantum state description given by the pseudo-spin, iso-spin and electron-hole symmetry is theoretically expected to be valid in both systems. Indeed, both materials show a strong suppression of backscattering (leading to high electron mobilities) and are believed to have exceptionally long spin coherence times due to weak spin-orbit interactions (light weight of carbon) and the low nuclear spin concentration, arising from the ~99% natural abundance of 12C. However, there are topological differences between the cylindrical nanotube and the flat graphene nanoribbon (Fig. 1), which may have significant impact on the dephasing of spin states for confined electrons. The recent work by F. Kuemmeth and co-workers [12] impressively demonstrates that spin-orbit interactions in nanotube quantum dots can be significant, Delta_SO = 1.9 meV/d[nm] (where d is the nanotube diameter), indicating that the spin coherence time might be severely shorter for carbon nanotubes than expected.

Since the origin of this spin-orbit coupling is directly related to the cylindrical topology of the nanotube, where the electron accumulates a spin-dependent topological flux for each rotation along the tube circumference, in an ideally flat graphene nanoribbon such flux accumulating tra jectories should not be present and there is a legitimate hope for much weaker spin-orbit coupling in graphene quantum dots. So far, no corresponding experimental data for graphene quantum dots has been reported. It is not clear whether the presence of spin-orbit coupling in nanotubes will be a blessing or a curse for a quantum dot qubit. It may permit "topologically" protected spin-orbit quibts [12], which actually may allow manipulation of the qubit state via an external electric field, or may simply lead to much shorter spin coherence times than equivalent graphene quantum dots. While it remains to be seen whether nanotubes or graphene offer the best way forward, it appears that these seemingly similar materials will eventually require utterly different design rules for implementing and manipulating qubits. Up to now there is a huge arena for opportunities and let's just hope that one or even both nanotubes and graphene will lead to useful qubit systems.

References
[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, Science, 306, 666 (2004).
[2] For review see: A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007), and A. H. Castro Neto, F. Guinea, N. M. Peres, A.K. Geim, cond-mat 0709.1163v1 (2007).
[3] M. Ieong, B. Doris, K. Kedzierski, K. Rim and M. Yang, Science, 306, 2057 (2004).
[4] Nielsen, Michael and Isaac Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press. ISBN 0-521-63503-9 (2000).
[5] D. Loss and D. P. DiVincenzo, Phys. Rev. A, 57, 120 (1998).
[6] Z. Chen, Y. Lin, M. Rooks and P. Avouris, Physica E, 40, 228 (2007).
[7] M. Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett., 98, 206805 (2007).
[8] C. Stampfer, J. Guettinger, F. Molitor, D. Graf, T. Ihn, and K. Ensslin, Appl. Phys. Lett., 92, 012102 (2008).
[9] L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. H. Hill, K. S. Novoselov, and A. K. Geim, cond-mat 0801.0160 (2008).
[10] X. Li, X. Wang, L. Zhang, S. Lee, H. Dai, Science, 319, 1229 (2008).
[11] For review see e.g.: S. Sapmaz, P. Jarillo-Herrero, L. P. Kouwenhoven and H. S. J. van der Zant, Semicond. Sci. Technol. 21, 52-63 (2008).
[12] F. Kuemmeth, S. Ilani, D. C. Ralph and P. L. McEuen, Nature, 452, 448 (2008).
* Figure courtesy of J. Meyer