Parallel 2-Qubit Operations on a Programmable Ion Trap Quantum Computer*

Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. We present experimental results for a pair of 2-qubit gates performed simultaneously in a single chain of trapped ions. The system used is a programmable quantum computer consisting of a linear chain of five trapped $^{171}$Yb$^+$ atomic clock ions with long coherence times. We employ a pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit XX gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the interaction produced yields only spin-spin interactions between the desired pairs with neither residual spin-motion entanglement nor “crosstalk” spin-spin entanglement is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder [1] using a depth-4 circuit requiring the use of parallel 2-qubit operations [2] as well as modular 1- and 2-qubit operations previously demonstrated on this system [3]. [1] Opt. News, 11, 11–20 (1985), [2] IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., 27(3):436-444 (2008), [3] Nature 536, 63 (2016).