Chiaverini, J.; Britton, J.; Leibfried, D.; Knill, E.; Barrett, M. D.; Blakestad, R. B.; Itano, W. M.; Jost, J. D.; Langer, C.; Ozeri, R.; Schaetz, T.; Wineland, D. J. Implementation of the semiclassical quantum Fourier transform in a scalable system. (English) Zbl 1226.81045 Science 308, No. 5724, 997-1000 (2005). Summary: We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor’s algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state’s amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm. Cited in 15 Documents MSC: 81P68 Quantum computation 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 81-05 Experimental work for problems pertaining to quantum theory PDFBibTeX XMLCite \textit{J. Chiaverini} et al., Science 308, No. 5724, 997--1000 (2005; Zbl 1226.81045) Full Text: DOI