Grover's algorithm on two-way quantum computer

TL;DR

This paper investigates how two-way quantum computing (2WQC) affects Grover's algorithm, showing that 2WQC can achieve constant complexity in ideal conditions and is more noise-resilient than standard Grover's algorithm.

Contribution

It introduces the analysis of Grover's algorithm within the 2WQC framework and compares its noise resilience to the standard approach.

Findings

2WQC Grover's algorithm has constant complexity $\\mathcal{O}(1)$ in ideal conditions.

2WQC Grover's algorithm is more resilient to noise than standard Grover's algorithm.

In noisy environments, 2WQC maintains better performance than traditional methods.

Abstract

Two-way quantum computing (2WQC) represents a novel approach to quantum computing that introduces a CPT version of state preparation. This paper analyses the influence of this approach on Grover's algorithm and compares the behaviour of typical Grover and its 2WQC version in the presence of noise in the system. Our findings indicate that, in an ideal scenario without noise, the 2WQC Grover algorithm exhibits a constant complexity of $\mathcal{O}(1)$. In the presence of noise, the 2WQC Grover algorithm demonstrates greater resilience to different noise models than the standard Grover's algorithm.