  The circuit model of quantum computation can be interpreted as a scattering
process. In particular, factorised scattering operators result in integrable
quantum circuits that provide universal quantum computation and are potentially
less noisy. These are realized through Yang-Baxter or 2-simplex operators. A
natural question is to extend this construction to higher qubit gates, like the
Toffoli gates, which also lead to universal quantum computation but with
shallower circuits. We show that unitary families of such operators are
constructed by the 3-dimensional generalizations of the Yang-Baxter operators
known as tetrahedron or 3-simplex operators. The latter satisfy a spectral
parameter-dependent tetrahedron equation. This construction goes through for
$n$-Toffoli gates realized using $n$-simplex operators.
