A small trapped-ion quantum register

We review experiments performed at the National Institute of Standards and Technology on entanglement, Bell's inequality and decoherence-free subspaces (DFSs) in a quantum register of trapped Be-9(+) ions. The group of Dr David Wineland has demonstrated entanglement of up to four ions using the technique of Molmer and Sorensen. This method produces the state (\down arrowdown arrow> + \up arrowup arrow>)/root2 for two ions and the state (\down arrowdown arrowdown arrowdown arrow> + \up arrowup arrowup arrowup arrow>)/root2 for four ions. The entanglement was generated deterministically in each shot of the experiment. Measurements on the two-ion entangled state violate Bell's inequality at the 8sigma level. Because of the high detector efficiency of the apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. The group also demonstrated measurement of an interferometric phase with precision better than the shot-noise limit using a two-ion entangled state. A large-scale version of this scheme could improve the signal-to-noise ratio of atomic clocks by orders of magnitude. Further experiments demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a DFS of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic. Finally, we describe an architecture for a large-scale ion trap quantum computer. By performing logic gates on small numbers of ions trapped in separate regions of the array, we take advantage of existing techniques for manipulating small trapped-ion quantum registers while enabling massively parallel gate operation. Encoding the quantum information in the DFS removes decoherence associated with ion transport and imperfect clock synchronization.