Generalized Toffoli gates using qudit catalysis
Radu Ionicioiu, Timothy P. Spiller, William J. Munro · Physical Review A · 2009
We present quantum networks for a $n$-qubit controlled gate ${C}^{n\ensuremath{-}1}(U)$ which use a higher-dimensional (qudit) ancilla as a catalyzer. In its simplest form the network has only $n$ two-particle gates (qubit-qudit)---this is the minimum number of two-body interactions needed to couple all $n+1$ subsystems ($n$ qubits plus one ancilla). This class of controlled gates includes the generalized Toffoli gate ${C}^{n\ensuremath{-}1}(X)$ on $n$ qubits, which plays an important role in several quantum algorithms and error correction. A particular example implementing this model is given by the dispersive limit of a generalized Jaynes-Cummings Hamiltonian of an effective spin $s$ interacting with a cavity mode.