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Implementation of the semiclassical quantum Fourier transform in a scalable system. (English) Zbl 1226.81045

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.

MSC:

81P68 Quantum computation
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
81-05 Experimental work for problems pertaining to quantum theory
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