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arXiv:0910.1023 · Physical Review A

Design of quantum Fourier transforms and quantum algorithms by using circulant Hamiltonians

Boyan T. Torosov, Nikolay V. Vitanov

Published Aug 21, 2009• 9 citations
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Abstract

We propose a technique for design of quantum Fourier transforms, and ensuing quantum algorithms, in a single interaction step by engineered Hamiltonians of circulant symmetry. The method uses adiabatic evolution and is robust against fluctuations of the interaction parameters as long as the Hamiltonian retains a circulant symmetry.
DOI
10.1103/physreva.80.022329

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Abstract Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in the Hamiltonian and as a result the entanglement will be maintained. The realization will be leaned on trapped ions and the gate implementation requires an adiabatic transition from each spin product state to Fourier modes. The fidelity was numerically calculated and the results show important values. Finally, we discuss the acceleration of the gate by using the counter-driving field.
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