Reducing the number of ancilla qubits and the gate count required for creating large controlled operations

Abstract

In this paper, we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. (Phys Rev A 75:022313, 2007) to be applicable to qubits. While this scheme requires more gates than standard schemes for creating large controlled gates, we show that with simple adaptations, it is directly equivalent to the standard scheme in the literature. This scheme is the most gateefficient way of creating large controlled unitaries currently known; however, it is expensive in terms of the number of ancilla qubits used. We go on to show that using a combination of these standard techniques presented by Barenco et al. (Phys Rev A 52(5): 3457, 1995), we can create an n-qubit version of the Toffoli using less gates and the same number of ancilla qubits as recent work using computer optimization. This would be useful in any architecture of quantum computing where gates are cheap but qubit initialization is expensive.