Scaling and Better Approximating Quantum Fourier Transform by Higher Radices

Abstract

Quantum Fourier transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can be built is limited, while many quantum technologies are inherently three (or more) valued, we consider extending the reach of the realistic quantum systems by building a QFT over ternary quantum digits. Compared to traditional binary QFT, the q-valued transform improves approximation properties and increases the state space by a factor of (q/2) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . Further, we use nonbinary QFT derivation to generalize and improve the approximation bounds for QFT