Generalized Toffoli gates using qudit catalysis

We present quantum networks for a n-qubit controlled gate C^n-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-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.