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Quantum search algorithms

A. Ambainis
2004 ACM SIGACT News  
Grover's search and amplitude amplification Grover's search algorithm is one of main quantum algorithms. The problem that it solves is very simple to state:  ...  We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the  ...  We give three examples of quantum algorithms of this type, one very simple and two more advanced ones.  ... 
doi:10.1145/992287.992296 fatcat:en627k5ovvd35prsjp3kxlyo3q

Quantum search algorithms [article]

Andris Ambainis
2005 arXiv   pre-print
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the  ...  recent quantum algorithms based on quantum walks.  ...  We give three examples of quantum algorithms of this type, one very simple and two more advanced ones.  ... 
arXiv:quant-ph/0504012v1 fatcat:fhgxsjvri5h67a7zjgjpuiyhpi

Quantum Algorithms: Database Search and its Variations [article]

Apoorva Patel
2011 arXiv   pre-print
Research on the subject has unraveled several aspects of how that can happen.  ...  Clever quantum algorithms have been discovered in recent years, although not systematically, and the field remains under active investigation.  ...  Complexity of quantum spatial search on a hypercubic lattice obeys two simple lower bounds.  ... 
arXiv:1102.2058v1 fatcat:ujaoeopcmbbjrnokgensaojdoy

Improving the query complexity of quantum spatial search in two dimensions [article]

Abhijith J., Apoorva Patel
2018 arXiv   pre-print
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem.  ...  An important ingredient of our algorithm is the implementation of multi-step quantum walks by graph powering, using a coin space of walk-length dependent dimension, which may be of independent interest  ...  Two query complexities The quantum spatial search algorithms of AKR [3] and Tulsi [18] work by alternatively applying a local walk operator (W ) and an oracle operator (O) that marks the target state  ... 
arXiv:1810.12600v1 fatcat:hdnpoesnmzddffr6hzj5k2lwji

Quantum Separation of Local Search and Fixed Point Computation

Xi Chen, Xiaoming Sun, Shang-Hua Teng
2009 Algorithmica  
It can also be extended to the quantum model for Sperner's Lemma in any dimensions: The quantum query complexity of finding a panchromatic cell in a Sperner coloring of a uniform triangulation of a d-dimensional  ...  In this paper, we give a lower bound of Ω(n (d−1)/2 ) on the quantum query complexity for finding a fixed point of a discrete Brouwer function over grid [1 : n] d .  ...  Final Remarks and Open Questons It remains open whether the quantum query complexity of fixed point computation over [1 : n] d is indeed Θ(n d/2 ) or a better algorithm with quantum query complexity Θ(  ... 
doi:10.1007/s00453-009-9289-0 fatcat:c363o34j5fezvpyql7gpu7n25e

On the Quantum Complexity of Closest Pair and Related Problems [article]

Scott Aaronson, Nai-Hui Chia, Han-Hsuan Lin, Chunhao Wang, Ruizhe Zhang
2020 arXiv   pre-print
Specifically, we give an Õ(n^2/3) algorithm in constant dimensions, which is optimal up to a polylogarithmic factor by the lower bound on the quantum query complexity of element distinctness.  ...  This paper asks and answers the question of the problem's quantum time complexity.  ...  Acknowledgements We would like to thank Lijie Chen and Pasin Manurangsi for helpful discussion. We would like to thank anonymous reviewers for their valuable suggestions on this paper.  ... 
arXiv:1911.01973v2 fatcat:wcmux2zd7rbrdoccnlx5b2kepe

Geometric and quantum methods for information retrieval

Yaoyong Li, Hamish Cunningham
2008 SIGIR Forum  
The purpose of the paper is to give the state of the art on and to draw attention of the IR community to the geometric and quantum methods and their potential applications in IR and NLP.  ...  It also presents the applications of the concepts and methods in quantum mechanics such as quantum logic and tensor product to document retrieval and meaning of composite words, respectively.  ...  Acknowledgements: We would like to thank our colleague Adam Funk for help improving the English of the manuscript. This work was supported by the EU-founded project LarKC, http://www.larkc.eu/.  ... 
doi:10.1145/1480506.1480510 fatcat:touvnagimjfcvfzfj7z3yjlivi

Realizable quantum adiabatic search

I. Hen
2017 Europhysics letters  
By studying the scaling of the gap and relevant matrix element in various spatial dimensions, we show that a quantum speedup can already be gained in three dimensions.  ...  Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones.  ...  We thank Tameem Albash, Mohammad Amin, Daniel Lidar, Eleanor Rieffel and Marcos Rigol for useful comments and discussions.  ... 
doi:10.1209/0295-5075/118/30003 fatcat:regkkolq6rhy5pogktskgqt6wi

New upper and lower bounds for randomized and quantum local search

Shengyu Zhang
2006 Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06  
and QLS(G) are the randomized and quantum query complexities of Local Search on G, respectively.  ...  This improves the previous best known upper bound of O(n 2/3 ) (Aaronson, [2]), and implies that Local Search on grids exhibits different properties in low dimensions.  ...  Thanks also to Yves Verhoeven and Dirk Winkler for each pointing out an error in a preliminary version of the paper.  ... 
doi:10.1145/1132516.1132605 dblp:conf/stoc/Zhang06 fatcat:p3bnovclyzf4rlmruyrribvvsm

Lower bounds for local search by quantum arguments

Scott Aaronson
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension greater than 2. *  ...  The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms.  ...  Acknowledgments I thank David Aldous, James Lee, Christos Papadimitriou, Yuval Peres, Craig Tovey, Umesh Vazirani, Avi Wigderson, and Ronald de Wolf for helpful discussions.  ... 
doi:10.1145/1007352.1007358 dblp:conf/stoc/Aaronson04a fatcat:agnw3uejfffc5l5o3zt2gzmpbq

Lower Bounds for Local Search by Quantum Arguments

Scott Aaronson
2006 SIAM journal on computing (Print)  
Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension greater than 2. *  ...  The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms.  ...  Acknowledgments I thank David Aldous, James Lee, Christos Papadimitriou, Yuval Peres, Craig Tovey, Umesh Vazirani, Avi Wigderson, and Ronald de Wolf for helpful discussions.  ... 
doi:10.1137/s0097539704447237 fatcat:o7yhleurebaolg7v2dkprjsr2u

A Survey of Quantum Theory Inspired Approaches to Information Retrieval [article]

Sagar Uprety and Dimitris Gkoumas and Dawei Song
2020 arXiv   pre-print
This paper presents a survey of the research done in this area, aiming to show the landscape of the field and draw a road-map of future directions.  ...  Since 2004, researchers have been using the mathematical framework of Quantum Theory (QT) in Information Retrieval (IR). QT offers a generalized probability and logic framework.  ...  The authors are hopeful that this literature survey is able to provide a clear picture of the quantum-inspired IR field and set a road-map for researchers to take this field forward.  ... 
arXiv:2007.04357v1 fatcat:uc6mi6mlizfivk2v3reb474s4q

Reinforcement Learning-driven Information Seeking: A Quantum Probabilistic Approach [article]

Amit Kumar Jaiswal, Haiming Liu, Ingo Frommholz
2020 arXiv   pre-print
Also, our framework incorporates the inherent uncertainty of the foragers' action using the mathematical formalism of quantum mechanics.  ...  Although information spread in uncertain information space is substantially complex due to the high entanglement of users interacting with information objects~(text, image, etc.).  ...  Acknowledgements This work is part of the Quantum Access and Retrieval Theory (QUARTZ) project, which has received funding from the European Union's Horizon 2020 research and innovation programme under  ... 
arXiv:2008.02372v1 fatcat:yyw6ria3fjcrljphlf76cbrn7q

New upper and lower bounds for randomized and quantum Local Search [article]

Shengyu Zhang
2006 arXiv   pre-print
Here RLS(G) and QLS(G) are the randomized and quantum query complexities of Local Search on G, respectively.  ...  This improves the previous best known upper bound of O(n^2/3) (Aaronson, [STOC'04]), and implies that Local Search on grids exhibits different properties in low dimensions.  ...  Thanks also to Yves Verhoeven and Dirk Winkler for each pointing out an error in a preliminary version of the paper.  ... 
arXiv:quant-ph/0603034v1 fatcat:fb7bi45tsngoxnw66ct7p2erzq

Searching via walking: How to find a marked clique of a complete graph using quantum walks

Mark Hillery, Daniel Reitzner, Vladimír Bužek
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
If the complete graph has N vertices and the subgraph has K vertices, the particle becomes localized on the subgraph in O(N/K) steps.  ...  We show how to implement the quantum walk using a quantum circuit and a quantum oracle, which allows us to specify the resource needed for a quantitative comparison of the efficiency of classical and quantum  ...  As each step of the walk involves only two oracle calls, and with the number of oracle calls being a measure of the complexity of the problem, we conclude that fewer oracle calls are needed in the quantum  ... 
doi:10.1103/physreva.81.062324 fatcat:lk2kwjjbrfe7vbjj7pm2tqluw4
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