  Numerical simulation results are presented which suggest that a class of
non-adiabatic rapid passage sweeps first realized experimentally in 1991 should
be capable of implementing a universal set of quantum gates G_{u} that operate
with high fidelity. The gates constituting G_{u} are the Hadamard and NOT
gates, together with variants of the phase, \pi /8, and controlled-phase gates.
The universality of G_{u} is established by showing that it can construct the
universal set consisting of Hadamard, phase, \pi /8, and controlled-NOT gates.
Sweep parameter values are provided which simulations indicate will produce the
different gates in G_{u}, and for which the gate error probability P_{e}
satisfies: (i) P_{e} < 10^{-4} for the one-qubit gates; and (ii) P_{e} < 1.27x
10^{-3} for the modified controlled-phase gate. The sweeps in this class are
non-composite and generate controllable quantum interference effects that allow
the gates in G_{u} to operate non-adiabatically while maintaining high
fidelity. These interference effects have been observed using NMR, and it has
previously been shown how these rapid passage sweeps can be applied to atomic
systems using electric fields. Here we show how these sweeps can be applied to
both superconducting charge and flux qubit systems. The simulations suggest
that the universal set of gates G_{u} produced by these rapid passage sweeps
shows promise as possible elements of a fault-tolerant scheme for quantum
computing.
