  Being able to quantify the level of coherent control in a proposed device
implementing a quantum information processor (QIP) is an important task for
both comparing different devices and assessing a device's prospects with
regards to achieving fault-tolerant quantum control. We implement in a
liquid-state nuclear magnetic resonance QIP the randomized benchmarking
protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error
per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a
single qubit QIP and show an experimentally relevant error model where the
randomized benchmarking gives a signature fidelity decay which is not possible
to interpret as a single error per gate. We explore and experimentally
investigate multi-qubit extensions of this protocol and report an average error
rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three
qubit QIP. We estimate that these error rates are still not decoherence limited
and thus can be improved with modifications to the control hardware and
software.
