Quantum arithmetic operations based on quantum Fourier transform on signed integers

Abstract

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two's complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.

23 pages, 38 figures, Accepted by International Journal of Quantum Information on Sep 3, 2020, Online Ready on Oct 8, 2020

References in corpus (1)

• A new quantum ripple-carry addition circuit

Cited by in corpus (5)

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• Optimized synthesis of circuits for diagonal unitary matrices with reflection symmetry
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• Performance Evaluations of Signed and Unsigned Noisy Approximate Quantum Fourier Arithmetic