  Quantum gates are the building blocks of quantum circuits, which in turn are
the cornerstones of quantum information processing. In this work, we
theoretically investigate a single-step implementation of both a universal two-
(CNOT) and three-qubit (quantum Fredkin) gates in a cross-cavity setup coupled
to a $\Lambda$-type three-level atom. Within a high-cooperativity regime, the
system exhibits an atomic-state-dependent $\pi$-phase gate involving the
two-mode single-photon bright and dark states of the input light pulses. This
allows for the controlled manipulation of light states by the atom and vice
versa. Our results indicate these quantum gates can be implemented with high
probability of success using the state-of-the-art parameters, either for the
weak- or strong-coupling regime, where the quantum interference is due to an
electromagnetically-induced-transparency-like phenomenon and the Autler-Townes
splitting, respectively. This work not only paves the way for implementing
quantum gates in a single step using simple resources, thus avoiding the need
to chain basic gates together in a circuit, but it also endorses the potential
of cross-cavity systems for realizing universal quantum computation.
