Variational Quantum Algorithm based circuit that implements the Toffoli gate with multi inputs

Abstract: The prime objective of this study is to seek a circuit diagram for a multi-inputs Toffoli gate including only single qubit gates and CNOTs. In this regard, we have developed two variational quantum algorithms that can be used to implement a multi-inputs Toffoli gate. The cost functions of these two VQAs are derived by using the Hilbert Schmidt inner product and the expected value of an observable that can capture the difference between the inputs and outputs of a Toffoli gate. We employ two ansatz circuit architectures and use the PennyLane package to execute the optimization.