  Due to the technical difficulty of building large quantum computers, it is
important to be able to estimate how faithful a given implementation is to an
ideal quantum computer. The common approach of completely characterizing the
computation process via quantum process tomography requires an exponential
amount of resources, and thus is not practical even for relatively small
devices. We solve this problem by demonstrating that twirling experiments
previously used to characterize the average fidelity of quantum memories
efficiently can be easily adapted to estimate the average fidelity of the
experimental implementation of important quantum computation processes, such as
unitaries in the Clifford group, in a practical and efficient manner with
applicability in current quantum devices. Using this procedure, we demonstrate
state-of-the-art coherent control of an ensemble of magnetic moments of nuclear
spins in a single crystal solid by implementing the encoding operation for a 3
qubit code with only a 1% degradation in average fidelity discounting
preparation and measurement errors. We also highlight one of the advances that
was instrumental in achieving such high fidelity control.
