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Quantum arithmetic with the quantum Fourier transform

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Abstract

The quantum Fourier transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing quantum Fourier transform adders and multipliers and comment some simple variations that extend their capabilities. These modified circuits can perform modular and non-modular arithmetic operations and work with signed integers. Among the operations, we discuss a quantum method to compute the weighted average of a series of inputs in the transform domain. One of the circuits, the controlled weighted sum, can be interpreted as a circuit to compute the inner product of two data vectors.

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Acknowledgements

L. Ruiz-Perez has been funded by the FPI fellowship programme of the Spanish Ministry of Economy, Industry and Competitiveness (Grant BES-2015-074514). J.C. Garcia-Escartin has been funded by Project TEC2015-69665-R (MINECO/FEDER, UE) and Junta de Castilla y León Project No. VA089U16.

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Correspondence to Lidia Ruiz-Perez.

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Ruiz-Perez, L., Garcia-Escartin, J.C. Quantum arithmetic with the quantum Fourier transform. Quantum Inf Process 16, 152 (2017). https://doi.org/10.1007/s11128-017-1603-1

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