Quantum search algorithm on weighted databases

• URL: http://arxiv.org/abs/2312.01590v3
• Date: Tue, 03 Dec 2024 09:46:42 GMT
• Title: Quantum search algorithm on weighted databases
• Authors: Yifan Sun, Lian-Ao Wu,
• Abstract summary: Grover algorithm is a crucial solution for addressing unstructured search problems. This research extensively investigates Grover's search methodology within non-uniformly distributed databases.
• Score: 5.229564709919574
• License:
• Abstract: The Grover algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research extensively investigates Grover's search methodology within non-uniformly distributed databases, a scenario frequently encountered in practical applications. Our analysis reveals that the behavior of the Grover evolution differs significantly when applied to non-uniform databases compared to uniform or 'unstructured databases'. Based on the property of differential equation, it is observed that the search process facilitated by this evolution does not consistently result in a speed-up, and we have identified specific criteria for such situations. Furthermore, we have extended this investigation to databases characterized by coherent states, confirming the speed-up achieved through Grover evolution via rigorous numerical verification. In conclusion, our study provides an enhancement to the original Grover algorithm, offering insights to optimize implementation strategies and broaden its range of applications.

Related papers

• A Learning Search Algorithm for the Restricted Longest Common Subsequence Problem [40.64116457007417]
  The Restricted Longest Common Subsequence (RLCS) problem has significant applications in bioinformatics. This paper introduces two novel approaches designed to enhance the search process by steering it towards promising regions. An important contribution of this paper is found in the generation of real-world instances where scientific abstracts serve as input strings.
  arXiv  Detail & Related papers  (2024-10-15T20:02:15Z)
• Topological Analysis for Detecting Anomalies (TADA) in Time Series [3.040934280444531]
  The proposed approach is lean enough to handle large scale datasets, and extensive numerical experiments back the intuition that it is more suitable for detecting global changes of correlation structures than existing methods. Some theoretical guarantees for quantization algorithms based on dependent time sequences are also provided.
  arXiv  Detail & Related papers  (2024-06-10T11:03:40Z)
• Biased Random-Key Genetic Algorithms: A Review [2.4578723416255754]
  The review encompasses over 150 papers with a wide range of applications. Scheduling is by far the most prevalent application area in this review, followed by network design and location problems. The most frequent hybridization method employed is local search, and new features aim to increase population diversity.
  arXiv  Detail & Related papers  (2023-12-01T22:32:58Z)
• Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors [58.340159346749964]
  We propose a new neural-symbolic method to support end-to-end learning using complex queries with provable reasoning capability. We develop a new dataset containing ten new types of queries with features that have never been considered. Our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.
  arXiv  Detail & Related papers  (2023-04-14T11:35:35Z)
• Research Trends and Applications of Data Augmentation Algorithms [77.34726150561087]
  We identify the main areas of application of data augmentation algorithms, the types of algorithms used, significant research trends, their progression over time and research gaps in data augmentation literature. We expect readers to understand the potential of data augmentation, as well as identify future research directions and open questions within data augmentation research.
  arXiv  Detail & Related papers  (2022-07-18T11:38:32Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions [17.097192646470372]
  We introduce several strategies to improve the scalability of exact score-based methods in the linear Gaussian setting. We develop a super-structure estimation method based on the support of inverse covariance matrix which requires assumptions that are strictly weaker than faithfulness. We also propose a local search strategy that performs exact search on the local clusters formed by each variable and its neighbors within two hops in the super-structure.
  arXiv  Detail & Related papers  (2022-01-14T20:52:30Z)
• Multidimensional Assignment Problem for multipartite entity resolution [69.48568967931608]
  Multipartite entity resolution aims at integrating records from multiple datasets into one entity. We apply two procedures, a Greedy algorithm and a large scale neighborhood search, to solve the assignment problem. We find evidence that design-based multi-start can be more efficient as the size of databases grow large.
  arXiv  Detail & Related papers  (2021-12-06T20:34:55Z)
• Grover search revisited; application to image pattern matching [0.8367938108534343]
  We propose a quantum algorithm that approximately executes the entire Grover database search or pattern matching algorithm. The key idea is to use the recently proposed approximate amplitude encoding method on a shallow quantum circuit.
  arXiv  Detail & Related papers  (2021-08-24T17:30:41Z)
• Redefining Neural Architecture Search of Heterogeneous Multi-Network Models by Characterizing Variation Operators and Model Components [71.03032589756434]
  We investigate the effect of different variation operators in a complex domain, that of multi-network heterogeneous neural models. We characterize both the variation operators, according to their effect on the complexity and performance of the model; and the models, relying on diverse metrics which estimate the quality of the different parts composing it.
  arXiv  Detail & Related papers  (2021-06-16T17:12:26Z)
• Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms [71.62575565990502]
  We prove that the generalization error of an optimization algorithm can be bounded on the complexity' of the fractal structure that underlies its generalization measure. We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden/layered neural networks) and algorithms.
  arXiv  Detail & Related papers  (2021-06-09T08:05:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.