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Implementation of the semiclassical quantum Fourier transform in a scalable system



J Chiaverini, Joseph W. Britton, Dietrich G. Leibfried, Emanuel H. Knill, Murray D. Barrett, Brad R. Blakestad, Wayne M. Itano, John D. Jost, C. Langer, R Ozeri, Tobias Schaetz, David J. Wineland


One of the most interesting future applications of quantum computers is Shor's factoring algorithm, which provides an exponential speedup compared to known classical algorithms. The crucial final step in Shor's algorithm is the quantum Fourier transform, which acts on a register of qubits (two-level quantum systems) to determine the periodicity of the input state's amplitudes. In algorithms such as Shor's, the quantum Fourier transform is used to determine the periodicity of a set of quantum amplitudes. As only probability amplitudes are required for this task, a more efficient semiclassical version can be employed for which only single-qubit operations conditioned on measurement outcomes are required. The transform has been implemented in nuclear magnetic resonance systems but has not been demonstrated in a scalable system. Furthermore, the semiclassical version, which requires actions conditioned on previous measurements, could not be performed in these experiments. Here we describe the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits confined in a segmented multi-zone trap. We apply the transform to several input states of different periodicities. This demonstration suggests the feasibility of scaling the quantum Fourier transform to a larger number of ion qubits as required for a useful quantum factoring algorithm.


atom trapping and cooling, quantum algorithms, quantum computation, quantum Fourier transform, quantum quantum information processing, quantum superpositions, quantum-state engineering, trapped ions


Chiaverini, J. , Britton, J. , Leibfried, D. , Knill, E. , Barrett, M. , Blakestad, B. , Itano, W. , Jost, J. , Langer, C. , Ozeri, R. , Schaetz, T. and Wineland, D. (2005), Implementation of the semiclassical quantum Fourier transform in a scalable system, Science, [online], (Accessed June 10, 2023)
Created May 13, 2005, Updated January 27, 2020