Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2305.12300 · Physical Review Research

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

Jian Leng, Fan Yang, Xiang‐Bin Wang

Published Jun 29, 2023• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.5.023202

Related papers

Deterministic Grover search with a restricted oracle

Tanay Roy, Liang Jiang, David Schuster

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems.The original protocol is probabilistic, returning the desired result with significant probability on each query but, in general, requiring several iterations of the algorithm.We present a modified version to return the correct result with certainty without having user control over the quantum search oracle.Our deterministic, two-parameter "D2p" protocol utilizes generalized phase rotations replacing the phase inversions after a standard oracle query.The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps as in the original Grover's search enabling the same quadratic speedup.We also provide a visualization using the Bloch sphere for enhanced geometric intuition.

arXiv:2201.00091•Physical Review Research•Apr 21, 2022•60 citations

A Four-Phase Improvement of Grover’s Algorithm

Bo-wen Ma, Wan‐Su Bao, Tan Li +3 more

When applying Grover’s algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. A four-phase improvement of Grover’s algorithm is proposed to fix the deficiency, and the unitary and the phase-matching condition are also proposed. With this improved scheme, when the proportion of target is over 1/3, the probability of obtaining correct results is greater than 97.82% with only one iteration using two phases. When the computational complexity is , the algorithm can succeed with a probability no less than 99.63%.

Chinese Physics Letters•Jul 1, 2017•3 citations

Comparative analysis for Effect of Noise in Grover’s Quantum Search Algorithm

Dushyant Kumar, Balwinder Raj, Gurmohan Singh

Abstract In quantum computing, Grover's technique is extremely vulnerable to several kinds of quantum noise in practice, which can seriously impair its functionality. This study examines how the algorithm's success probabilities is affected by several types of noise, such as rotational error, thermal noise, Two-State Purity (TSP) error, decay and decoherence, and depolarization variables. The findings demonstrate that the algorithm can accomplish flawless amplification of the goal state with negligible mistakes in non-target states when it is executed without noise. The most notable decrease among the noise kinds is caused by decay and decoherence errors and depolarization factors, which lower the likelihood of correctly detecting the target state from 1.0 to roughly 0.885 and 0.968, respectively. Thermal noise, TSP error, and rotational error, on the other hand, have less severe impacts and result in lesser deviations in both target and non-target states. These results demonstrate how crucial quantum error correction and noise reduction techniques are to guaranteeing Grover's algorithm's scalability and dependability in noisy quantum environments. To fully utilize the algorithm's promise in practical applications on both present-day and next quantum technology, these issues must be mitigated.

•Dec 1, 2025•0 citations

Noise-tolerant Grover's algorithm via success-probability prediction

Jian Leng, Fan Yang, Xiang‐Bin Wang

We present theoretical and experimental studies on efficient quantum search with noise. We propose a noise-tolerant method that significantly reduces the running time and exponentially improves the error threshold with number of qubits for Grover's search. Experiments are implemented on different quantum computing setups, with all results clearly confirming the advantage of our noise-tolerant method to the original Grover's search. In one setup, our method produces quantum advantages while the original Grover's search does not. In another setup with smaller noise, our method produces a larger quantum advantage than the original Grover's search does.

arXiv:2306.10855•Physical Review Research•Jan 21, 2025•4 citations

An Improved Quantum Grover Algorithm

Baoyu Zheng

The algorithm proposed by Grover solves the unsorted database search problem with computation complexity of O(2～(1/2)n/m),where the size of database is N=2n and there is m target solutions.However,the successful probability of searching decreases rapidly,when the target solutions m is greater than N/4,And the algorithm is disabled when m is equal to N/2.This paper presents an improved Grover's algorithm,which can find the object with the successful probability at least 98.01% with one step when m is greater than N/4.

Journal of Nanjing University of Posts and Telecommunications•Jan 1, 2011•0 citations

Exact results on Quantum search algorithm

Saptarshi Roy Chowdhury, Swarupananda Pradhan

We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of number of iterations, two phase angles (α, \{beta}) and parameter ξ introduced in the off diagonal terms of the density matrix in a sense to capture the coherence present in the initial quantum register. We extend Li and Li's idea and show for the phase matching condition α = -\{beta} = 0.35π with two iterations and ξ = 1, we can achieve success probability >= 0.8 only with a knowledge about the lower bound of λ = 0.166 where λ is the ratio of marked to total number states in the database. Finally we quantify success probability of the algorithm with decrease in coherence of the initial quantum state against modest noise in this simple model.

arXiv:2207.09762•Jul 20, 2022•0 citations
The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to 100100%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.
Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems.The original protocol is probabilistic, returning the desired result with significant probability on each query but, in general, requiring several iterations of the algorithm.We present a modified version to return the correct result with certainty without having user control over the quantum search oracle.Our deterministic, two-parameter "D2p" protocol utilizes generalized phase rotations replacing the phase inversions after a standard oracle query.The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps as in the original Grover's search enabling the same quadratic speedup.We also provide a visualization using the Bloch sphere for enhanced geometric intuition.
When applying Grover’s algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. A four-phase improvement of Grover’s algorithm is proposed to fix the deficiency, and the unitary and the phase-matching condition are also proposed. With this improved scheme, when the proportion of target is over 1/3, the probability of obtaining correct results is greater than 97.82% with only one iteration using two phases. When the computational complexity is , the algorithm can succeed with a probability no less than 99.63%.
Abstract In quantum computing, Grover's technique is extremely vulnerable to several kinds of quantum noise in practice, which can seriously impair its functionality. This study examines how the algorithm's success probabilities is affected by several types of noise, such as rotational error, thermal noise, Two-State Purity (TSP) error, decay and decoherence, and depolarization variables. The findings demonstrate that the algorithm can accomplish flawless amplification of the goal state with negligible mistakes in non-target states when it is executed without noise. The most notable decrease among the noise kinds is caused by decay and decoherence errors and depolarization factors, which lower the likelihood of correctly detecting the target state from 1.0 to roughly 0.885 and 0.968, respectively. Thermal noise, TSP error, and rotational error, on the other hand, have less severe impacts and result in lesser deviations in both target and non-target states. These results demonstrate how crucial quantum error correction and noise reduction techniques are to guaranteeing Grover's algorithm's scalability and dependability in noisy quantum environments. To fully utilize the algorithm's promise in practical applications on both present-day and next quantum technology, these issues must be mitigated.
We present theoretical and experimental studies on efficient quantum search with noise. We propose a noise-tolerant method that significantly reduces the running time and exponentially improves the error threshold with number of qubits for Grover's search. Experiments are implemented on different quantum computing setups, with all results clearly confirming the advantage of our noise-tolerant method to the original Grover's search. In one setup, our method produces quantum advantages while the original Grover's search does not. In another setup with smaller noise, our method produces a larger quantum advantage than the original Grover's search does.
The algorithm proposed by Grover solves the unsorted database search problem with computation complexity of O(2～(1/2)n/m),where the size of database is N=2n and there is m target solutions.However,the successful probability of searching decreases rapidly,when the target solutions m is greater than N/4,And the algorithm is disabled when m is equal to N/2.This paper presents an improved Grover's algorithm,which can find the object with the successful probability at least 98.01% with one step when m is greater than N/4.
We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of number of iterations, two phase angles (α, \{beta}) and parameter ξ introduced in the off diagonal terms of the density matrix in a sense to capture the coherence present in the initial quantum register. We extend Li and Li's idea and show for the phase matching condition α = -\{beta} = 0.35π with two iterations and ξ = 1, we can achieve success probability >= 0.8 only with a knowledge about the lower bound of λ = 0.166 where λ is the ratio of marked to total number states in the database. Finally we quantify success probability of the algorithm with decrease in coherence of the initial quantum state against modest noise in this simple model.