How to realize a universal quantum gate with trapped ions
Ferdinand Schmidt‐Kaler, Hartmut Häffner, S. Gulde, Mark Riebe, Gavin P. T. Lancaster, T. Deuschle, Christoph Becher, W. Hänsel, Jürgen Eschner, Christian F. Roos, R. Blatt
We discuss possibilities of quantum manipulations of trapped ions from the perspective of quantum information processing. We show how from a restricted set of feasible microscopic interactions a physical implementation of an arbitrary unitary operator can be realized. An example is given for the discrete Fourier transform. The synthesis of operators enables to realize universal quantum gates to process unknown input qubits which can be encoded into vibrational levels of trapped ions. We discuss also problem of an arbitrary measurement which can be performed using quantum gates.
We propose a scalable ion trap architecture for universal quantum computation, which is composed of an array of ion traps with one ion confined in each trap. The neighboring traps are designed capable of merging into one single trap. The universal two-qubit SWAP gate is realized by direct collision of two neighboring ions in the merged trap, which induces an effective spin-spin interaction between two ions. We find that the collision-induced spin-spin interaction decreases with the third power of two ions' trapping distance. Even with a 200μm trapping distance between atomic ions in Paul traps, it is still possible to realize a two-qubit gate operation with speed in 0.1kHz regime. The speed can be further increased up into 0.1MHz regime using electrons with 10mm trapping distance in Penning traps.