Quantum gates by reverse engineering of a Hamiltonian

Alan C. Santos

Published 2017-01-07Version 1

Reverse engineering of Hamiltonian (REH) from an evolution operator is an useful technique for protocols of quantum control with potential applications to quantum information processing. In this paper we introduce a particular protocol to perform REH and we show as this scheme can be used to perform universal quantum computing by using minimal quantum resources (such as entanglement, interactions between more than two quits or auxiliary quits). Remarkable, while previous protocol requires three-quits interactions and auxiliary quits to implement such gates, our protocol requires just two-qubit interactions and no additional resource. We apply our results to show as implement the quantum Fourier transform (QFT) motived by its applicability to Shor's algorithm. By using this approach, we can obtain a large class of Hamiltonians that allow us implement single and two-quit gates necessary in subroutines of quantum circuits of quantum algorithms as, for example, the Shor's algorithm.