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In order to realize quantum logical operations, Quantum Computation (QC)requires that its basic tools and concepts obey the laws of physics. One of thefundamental concepts in QC is the conditional quantum dynamics \cite{barenco},some times called controlled-unitary operation \cite{kumar}, which isestablished by the conditional "If-Then" sentence. The best know example is thec-not gate, which operates on the computational basis as follows: \textit{Ifthe control qubit is set to $% |1>$, then apply the single qubit quantum NOTgate on the target. Otherwise, if the control qubit is set to $|0>$, then thetarget qubit is unchanged}. This gate represents the paradigm for theconditional quantum dynamics, where the flipping of the target qubit isconditioned to the state of the control qubit. Other gates have been defined ina similar way of conditional evolution; for instance, the control phase gates\cite{paulo1}. However, to the best of our knowledge, such conditional quantumdynamics has not been yet used to define the SWAP gate. Here we propose apossible conditional definition, in the form of If-Then sentence, to constructa SWAP gate in the case of two qubits. This definition suggests aclassification in two classes, which depends upon the number of qubits thathave to undergo a conditional quantum dynamics.

A proposal for a conditional definition of the Swap Gate