Quantum arithmetic with the quantum Fourier transform
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 nonmodular 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.
 Publication:

Quantum Information Processing
 Pub Date:
 June 2017
 DOI:
 10.1007/s1112801716031
 Bibcode:
 2017QuIP...16..152R
 Keywords:

 Quantum Fourier transform;
 Quantum adder;
 Quantum multiplier