Randomized Benchmarking of Multi-Qubit Gates

As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be sufficiently high to support arbitrarily long quantum computations. Randomized benchmarking already provides a platform-independent method for assessing the quality of one-qubit rotations. Here we describe an extension of this method to multi-qubit gates. We provide a platform-independent protocol for evaluating the performance of experimental Clifford unitaries, which form the basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped-ion two-qubit phase gates and one-qubit gates and found an error per random two-qubit Clifford unitary of $0.162 \pm 0.008$, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate at each step, we extracted an error per phase gate of $0.069 \pm 0.017$. We conducted these experiments with movable, sympathetically cooled ions in a multi-zone Paul trap - a system that can in principle be scaled to larger numbers of ions.