  Quantum computers promise to solve certain problems more efficiently than
their digital counterparts. A major challenge towards practically useful
quantum computing is characterizing and reducing the various errors that
accumulate during an algorithm running on large-scale processors. Current
characterization techniques are unable to adequately account for the
exponentially large set of potential errors, including cross-talk and other
correlated noise sources. Here we develop cycle benchmarking, a rigorous and
practically scalable protocol for characterizing local and global errors across
multi-qubit quantum processors. We experimentally demonstrate its practicality
by quantifying such errors in non-entangling and entangling operations on an
ion-trap quantum computer with up to 10 qubits, with total process fidelities
for multi-qubit entangling gates ranging from 99.6(1)% for 2 qubits to 86(2)%
for 10 qubits. Furthermore, cycle benchmarking data validates that the error
rate per single-qubit gate and per two-qubit coupling does not increase with
increasing system size.
