Optimizing the number of CNOT gates in one-dimensional nearest-neighbor quantum Fourier transform circuit

TL;DR

This paper presents a method to significantly reduce the number of costly CNOT gates in one-dimensional nearest-neighbor quantum Fourier transform circuits, enhancing efficiency for quantum algorithms on hardware with physical constraints.

Contribution

The study introduces a new construction for 1D nearest-neighbor QFT circuits that decreases CNOT gate count by approximately 60%, applicable to quantum amplitude estimation.

Findings

CNOT gate count reduced by ~60%

Method applicable to quantum amplitude estimation

Improved efficiency for hardware-constrained quantum circuits

Abstract

The physical limitations of quantum hardware often require nearest-neighbor qubit structures, in which two-qubit gates are required to construct nearest-neighbor quantum circuits. However, two-qubit gates are considered a major cost of quantum circuits because of their high error rate as compared with single-qubit gates. The controlled-not (CNOT) gate is the typical choice of a two-qubit gate for universal quantum circuit implementation together with the set of single-qubit gates. In this study, we construct a one-dimensional nearest-neighbor circuit of quantum Fourier transform (QFT), which is one of the most frequently used quantum algorithms. Compared with previous studies on n-qubit one-dimensional nearest-neighbor QFT circuits, it is found that our method reduces the number of CNOT gates by ~60%. Additionally, we showed that our results for the one-dimensional nearest-neighbor circuit can be applied to quantum amplitude estimation.