  Superposed orders of quantum channels have already been proved - both
theoretically and experimentally - to enable unparalleled opportunities in the
quantum communication domain. As a matter of fact, superposition of orders can
be exploited within the quantum computing domain as well, by relaxing the
(traditional) assumption underlying quantum computation about applying gates in
a well-defined causal order. In this context, we address a fundamental question
arising with quantum computing: whether superposed orders of single-qubit gates
can enable universal quantum computation. As shown in this paper, the answer to
this key question is a definitive "yes". Indeed, we prove that any two-qubit
controlled quantum gate can be deterministically realized, including the
so-called Barenco gate that alone enables universal quantum computation.
