Quantum arithmetic operations based on quantum fourier transform on signed integers


ŞAHİN E.

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, vol.18, no.6, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.1142/s0219749920500355
  • Title of Journal : INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
  • Keywords: Quantum computing, quantum addition, quantum subtraction, quantum multiplication, quantum division, quantum comparison, quantum exponentiation, CIRCUIT

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.