Direct randomized benchmarking for multi-qubit devices

Abstract: Benchmarking methods that can be adapted to multi-qubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on 1, 2, and 3 qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the $n$-qubit Clifford gates at its core have to be compiled into large circuits over the 1- and 2-qubit gates native to a device. As $n$ grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low $n$. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on 2 -- 5 qubits, using the publicly available IBMQX5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But it can be extended to processors with more qubits -- we present simulations on 10+ qubits -- and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, which includes tasks such as measuring an average CNOT error rate.