Implementing Quantum Algorithms with Modular Gates in a Trapped Ion Chain

We present experimental results on quantum algorithms performed using fully modular one- and two-qubit gates in a linear chain of 5 Yb$+$ ions. This is accomplished through arbitrary qubit addressing and manipulation from stimulated Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser[1]. The Raman beam pairs consist of one global beam and a set of counter-propagating individual addressing beams, one for each ion. This provides arbitrary single-qubit rotations as well as arbitrary selection of ion pairs for a fully-connected system of two-qubit modular XX-entangling gates implemented using a pulse-segmentation scheme[2]. We execute controlled-NOT gates with an average fidelity of 97.0{\%} for all 10 possible pairs. Programming arbitrary sequences of gates allows us to construct any quantum algorithm, making this system a universal quantum computer. As an example, we present experimental results for the Bernstein-Vazirani algorithm using 4 control qubits and 1 ancilla, performed with concatenated gates that can be reconfigured to construct all 16 possible oracles, and obtain a process fidelity of 90.3{\%}. [1] PRL 104, 140501 (2010), [2] PRL 112, 19502 (2014)