  We explore the implementation of pseudo-random single-qubit rotations and
multi-qubit pseudo-random circuits constructed only from Clifford gates and the
T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for
computations performed in a fault tolerant setting. For single-qubit rotations
the distribution of parameters found for unitaries constructed from Clifford
plus T quickly approaches that of random rotations and require significantly
fewer gates than the construction of arbitrary single-qubit rotations. For
Clifford plus T pseudo-random circuits we find an exponential convergence to a
random matrix element distribution and a Gaussian convergence to the higher
order moments of the matrix element distribution. These convergence rates are
insensitive to the number of qubits.
