2016/08/31 by Emmi Herterich, Erik Sjöqvist · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.94.052310
published as Phys. Rev. A 94, 052310 (2016) · Some amendments; journal reference added
arxiv created 2016/11/11 · arxiv updated 2016/11/14
Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. \bf 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a Λ-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level Λ-coupling structure, by utilizing carefully chosen laser pulses.