Grover's algorithm on two-way quantum computer

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.