  We introduce a single-number metric, quantum volume, that can be measured
using a concrete protocol on near-term quantum computers of modest size
($n\lesssim 50$), and measure it on several state-of-the-art transmon devices,
finding values as high as 16. The quantum volume is linked to system error
rates, and is empirically reduced by uncontrolled interactions within the
system. It quantifies the largest random circuit of equal width and depth that
the computer successfully implements. Quantum computing systems with
high-fidelity operations, high connectivity, large calibrated gate sets, and
circuit rewriting toolchains are expected to have higher quantum volumes. The
quantum volume is a pragmatic way to measure and compare progress toward
improved system-wide gate error rates for near-term quantum computation and
error-correction experiments.
