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Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a time-independent Hamiltonian that generates a given multi-qubit unitary. In particular, we execute a Variational Quantum Algorithm, whose ansatz is carefully chosen to be a sequence of appropriately parametrized unitaries describing at most two-qubit nearest neighbour interactions, dictating the target unitary. Subsequently, we apply our approach to simulate multi-qubit target gates, with and without stochastic noise. We demonstrate that our strategy allows us to implement a Toffoli gate with sufficiently high fidelity, as compared to the other similar techniques. Our approach is an example of the usage of quantum computing for the design of quantum computers.