Abstract Grover’s quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a resource to mitigate the effects of noise. In this scenario, the noise is modeled by a depolarizing channel, which coherently acts on the entire quantum register. We show that a quantum switch can significantly reduce the error in Grover’s search algorithm. We consider the success probability of finding the marked item as the sole quantifier of diminishing the effect of noise in the search space in the presence of quantum switch. We propose two frameworks for the application of quantum switches. In the first framework, we apply the superposition of channel’s orders in the form of a switch and do a post-selection at every iteration of the applications of the Grover operator. In the second framework, we delay this measurement and post-selection until the very end. The number of post selections is minimal in the second scenario, and hence the noise reduction can be attributed more to the presence of quantum switch. We illustrate with an example of significant advantage in the success probability of Grover’s algorithm using quantum switch.Abstract Grover’s quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a resource to mitigate the effects of noise. In this scenario, the noise is modeled by a depolarizing channel, which coherently acts on the entire quantum register. We show that a quantum switch can significantly reduce the error in Grover’s search algorithm. We consider the success probability of finding the marked item as the sole quantifier of diminishing the effect of noise in the search space in the presence of quantum switch. We propose two frameworks for the application of quantum switches. In the first framework, we apply the superposition of channel’s orders in the form of a switch and do a post-selection at every iteration of the applications of the Grover operator. In the second framework, we delay this measurement and post-selection until the very end. The number of post selections is minimal in the second scenario, and hence the noise reduction can be attributed more to the presence of quantum switch. We illustrate with an example of significant advantage in the success probability of Grover’s algorithm using quantum switch.

arXiv:2401.05866Journal of Physics A Mathematical and TheoreticalDec 13, 20248 citations

Introduction to Grover Algorithm

茂山下

Jun 1, 20110 citations

Grover's algorithm on two-way quantum computer

Grzegorz Czelusta, Verma, Dev Rishi, Wanjalkar, Govind

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.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.

arXiv:2406.09450Jun 12, 20240 citations

Improving D2p Grover's algorithm to reach performance upper bound under phase noise

Jian Leng, Fan Yang, Xiang‐Bin Wang

The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to $100%$ . However, the success probability of deterministic Grover's algorithm decreases in noisy environment. Here we improve the deterministic two-parameter (D2p) Grover's algorithm to reach the upper bound for success probability under phase noise. We prove that it is not possible to design any deterministic Grover's algorithm whose success probability is higher than our improved D2p protocol's under phase noise.The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to $100%$. However, the success probability of deterministic Grover's algorithm decreases in noisy environment. Here we improve the deterministic two-parameter (D2p) Grover's algorithm to reach the upper bound for success probability under phase noise. We prove that it is not possible to design any deterministic Grover's algorithm whose success probability is higher than our improved D2p protocol's under phase noise.

arXiv:2305.12300Physical Review ResearchJun 29, 20235 citations

\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.

The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to

100%

. However, the success probability of deterministic Grover's algorithm decreases in noisy environment. Here we improve the deterministic two-parameter (D2p) Grover's algorithm to reach the upper bound for success probability under phase noise. We prove that it is not possible to design any deterministic Grover's algorithm whose success probability is higher than our improved D2p protocol's under phase noise.