We present a general framework to approach the problem of finding time-independent dynamics generating target unitary evolutions. More specifically, given a target unitary gate G over a set of qubits, and a parametrized Hamiltonian of the form H(λ)=iλiσi with σi Hermitian operators over the qubits, we want to find a set of values λ0 such that exp(iH(λ0))=G. We show that this problem is equivalently stated as a set of conditions over the spectrum of H(λ), reducing the problem to an inverse eigenvalue problem. We show how to solve this problem in some physically relevant instances, like for example to find time-independent dynamics implementing Toffoli and Fredkin gates without the need for ancillary gates or effective evolutions.

© 2019 The Author(s)

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