Seminarium Fizyki Materii Skondensowanej

Geometric phases, generated by cyclic evolutions of quantum systems with degenerate groundstate providing qubit basis, offer realization of the non-Abelian statistics. As compared to dynamic gates, non-Abelian geometric control over such a qubit should benefit from tolerance to fluctuations. On the example of dynamically driven hole-spin 3/2 immersed in QED cavity we have shown that the interplay between the non-Abelian Berry phases generated by local time-dependent electrical fields and the shared photons allows for fast manipulation, detection, and long-range entanglement of the qubits. Moreover, we have demonstrated that owing to its geometrical structure, such a scheme is indeed robust against external noises. Additionally, we have confirmed that the found mechanism also applies to quantum dot qubits where single-gate holonomic operations are executed by (i) cyclic control of the position of confining potential on the two dimensional plane as well as by (ii) cyclic control of position along one dimension together with periodic change of spin-orbit interaction.