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Quantum search algorithms
2004
ACM SIGACT News
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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]
2005
arXiv
pre-print
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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]
2011
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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
2009
Algorithmica
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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]
2020
arXiv
pre-print
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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
2008
SIGIR Forum
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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
2017
Europhysics letters
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2016 pre-print arXiv:1612.06012v1 fatcat:hfacfqrc75cizccbici4tpwjlaOther Versions
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
2006
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
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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
2004
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
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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
2006
SIAM journal on computing (Print)
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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]
2020
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2006
arXiv
pre-print
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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
2010
Physical Review A. Atomic, Molecular, and Optical Physics
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2009 pre-print arXiv:0911.1102v1 fatcat:bldooqx6trgprnfahqxgv3yhsu
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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