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We present quantum networks for a n-qubit controlled gate C^{n-1}(U) whichuse a higher dimensional (qudit) ancilla as a catalyser. In its simplest formthe network has only n two-particle gates (qubit-qudit) -- this is the minimumnumber of two-body interactions needed to couple all n+1 subsystems (n qubitsplus one ancilla). This class of controlled gates includes the generalisedToffoli gate C^{n-1}(X) on n qubits, which plays an important role in severalquantum algorithms and error correction. A particular example implementing thismodel is given by the dispersive limit of a generalised Jaynes-CummingsHamiltonian of an effective spin-s interacting with a cavity mode.

Generalized Toffoli gates using qudit catalysis