3. GEOMETRICAL QUANTUM EVOLUTIONS

Various ways of quantum information processing have been theoretically developed, each one with its own merits. One interesting approach employs geometric ideas of holonomic evolutions, which generalise the so-called Berry phase, discovered some time ago by Michael Berry. The systems we consider in our research are parameterised by a control manifold, giving the possibility to change their Hamiltonians in a continuous fashion. Conditions necessary for performing universal quantum computation with holonomic evolutions can be stated in terms of the curvature associated to that control manifold. The main ideas employed here come from differential geometry and appear also in gauge theories.
Experimentally, the currently most promising setup for encoding and processing quantum information is ion trap quantum technology using geometrical evolutions for the performance of two qubit gates. Recently, these ideas lead to the development of especially fast and robust gate operations.
Within this area I am interested in improving the resilience of geometrical gates in terms of control errors and decoherence due to the influence of the environment. We plan to analyse how the geometrical evolutions, considered as paths in the control parametric space, scale in the case of a realistic quantum algorithm.

References:
[1] A. Shapere and F. Wilczek (1989), Geometric Phases in Physics, World Scientific, Singapore.
[2] J. Pachos and P. Zanardi (2001), Quantum Holonomies for Quantum Computing, Int. J. Mod. Phys. B15, 1257-1286, quant-ph/0007110.
[3] A. Ekert, M. Ericsson, P. Hayden, H. Inamori, J. A. Jones, D. K. L. Oi and V. Vedral, (2000), Geometric Quantum Computation, J. Mod. Opt. 47(14-15):2501-2513, quant-ph/0004015.
[4] J. Pachos (2000), Quantum Computation by Geometrical Means, AMS proceedings, quant-ph/0003150.
[5] D. J. Wineland et al. (2002), Quantum information processing with trapped ions, quant-ph/0212079.