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A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates [article]

Andrew M. Childs and Stacey Jeffery and Robin Kothari and Frederic Magniez
2013 arXiv   pre-print
We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity O(n^5/7), matching the best known upper bound (obtained via learning graphs) up to log factors.  ...  We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates.  ...  Acknowledgments We thank Aleksandrs Belovs for helpful discussions about our two different approaches to this problem.  ... 
arXiv:1302.7316v1 fatcat:zwdjdurqknbldo5ykyrfirncyi

Time-Efficient Quantum Walks for 3-Distinctness [chapter]

Aleksandrs Belovs, Andrew M. Childs, Stacey Jeffery, Robin Kothari, Frédéric Magniez
2013 Lecture Notes in Computer Science  
The second algorithm uses an extension of the quantum walk search framework that facilitates quantum walks with nested updates. Introduction Element Distinctness is a basic computational problem.  ...  We present two quantum walk algorithms for 3-Distinctness.  ...  Nested Updates We show how to implement efficient nested updates using the coin-dependent data framework.  ... 
doi:10.1007/978-3-642-39206-1_10 fatcat:whevi2trfrbalgl4xayov3m2ei

Nested Quantum Walks with Quantum Data Structures [chapter]

Stacey Jeffery, Robin Kothari, Frederic Magniez
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum  ...  Surprisingly, only classical data structures were considered before for searching via quantum walks.  ...  Acknowledgments The authors would like to thank Andrew Childs, Troy Lee, Ashwin Nayak and Miklos Santha for helpful discussions.  ... 
doi:10.1137/1.9781611973105.106 dblp:conf/soda/JefferyKM13 fatcat:3lhu2elwmbhspkcszgicjgxzmi

Near-Optimal Quantum Algorithms for String Problems [article]

Shyan Akmal, Ce Jin
2021 arXiv   pre-print
We design our algorithm by first giving a new classical divide-and-conquer algorithm in near-linear time based on exclusion rules, and then speeding it up quadratically using nested Grover search and quantum  ...  String Rotation can be solved by a quantum algorithm in n^1/2 + o(1) time, improving upon the recent Õ(n^3/4)-time algorithm by Wang and Ying (2020).  ...  We additionally thank Virginia Vassilevska Williams for several useful comments on the writeup of this paper.  ... 
arXiv:2110.09696v2 fatcat:v6rindfjrnchbllvjvtcpnalay

Improved Quantum Algorithm for Triangle Finding via Combinatorial Arguments [article]

François Le Gall
2014 arXiv   pre-print
Our result shows, for the first time, that in the quantum query complexity setting unweighted triangle finding is easier than its edge-weighted version, since for finding an edge-weighted triangle Belovs  ...  Our result also illustrates some limitations of the non-adaptive learning graph approach used to obtain the previous O(n^9/7) upper bound since, even over unweighted graphs, any quantum algorithm for triangle  ...  Acknowledgments The author is grateful to Harumichi Nishimura and Seiichiro Tani for stimulating discussions about the quantum complexity of triangle finding and several comments about this paper, and  ... 
arXiv:1407.0085v2 fatcat:it5egcbufngx3oabx56u4ipk3e

Improved Classical and Quantum Algorithms for Subset-Sum [article]

Xavier Bonnetain, Rémi Bricout, André Schrottenloher, Yixin Shen
2020 arXiv   pre-print
This time is dependent on a heuristic on quantum walk updates, formalized by Helm and May, that is also required by the previous algorithms.  ...  We also propose new quantum walks for subset-sum, performing better than the previous best time complexity of 𝒪̃(2^0.226 n) given by Helm and May (TQC 2018).  ...  Second, both use a conjecture (implicit in [6] , made explicit in [17] ) about quantum walk updates.  ... 
arXiv:2002.05276v4 fatcat:6qjtqwnelfg2zofuggfdeqqtfi

How to Compute Using Quantum Walks

Viv Kendon
2020 Electronic Proceedings in Theoretical Computer Science  
Quantum walks have also been shown to be universal for quantum computing.  ...  Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied.  ...  Thanks to Jemma Bennett and Stephanie Foulds for interesting discussions and checking the manuscript. A recording of the presentation of this work is available at [32] .  ... 
doi:10.4204/eptcs.315.1 fatcat:ns3qogqonrdkdikzmdm4h4vuf4

Quantum-enhanced deliberation of learning agents using trapped ions

V Dunjko, N Friis, H J Briegel
2015 New Journal of Physics  
In particular, classical random walks were substituted by Szegedy-type quantum walks, allowing for a speed-up.  ...  We employ a generic construction by which the classical agents are 'upgraded' to their quantum counterparts by nested coherent controlization, and we outline how this construction can be realized in ion  ...  Acknowledgments We are grateful to Adi Makmal, Markus Tiersch, Benjamin P Lanyon, Daniel Nigg and Thomas Monz for valuable discussions and comments.  ... 
doi:10.1088/1367-2630/17/2/023006 fatcat:lrcskofqsnennjncferhff4xxe

Cuckoo search: recent advances and applications

Xin-She Yang, Suash Deb
2013 Neural computing & applications (Print)  
Cuckoo search (CS) is a relatively new algorithm, developed by Yang and Deb in 2009, and CS is efficient in solving global optimization problems.  ...  We also discuss the essence of algorithms and its link to self-organizing systems, and finally we propose some important topics for further research.  ...  As mentioned in Section 3.1, the local search is very intensive with about 1/4 of the search time (for p a = 0.25), while global search takes about 3/4 of the total search time.  ... 
doi:10.1007/s00521-013-1367-1 fatcat:35e36tbfvnezrbfmtc7btvhrju


Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, Benoît Valiron
2013 SIGPLAN notices  
Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems.  ...  Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates.  ...  They make use of a wide variety of quantum primitives, such as amplitude amplification, quantum walks, the quantum Fourier transform, and quantum simulation.  ... 
doi:10.1145/2499370.2462177 fatcat:uuxftufbl5ettjwkw7coovfhsy

Faster quantum mixing for slowly evolving sequences of Markov chains [article]

Davide Orsucci, Hans J. Briegel, Vedran Dunjko
2018 arXiv   pre-print
We provide a quantum memory-efficient algorithm with a run-time of O(√(δ^-1)√(N)), neglecting logarithmic terms, which is an important improvement for large state spaces.  ...  However, except in special cases, quantum algorithms achieve a run-time of O(√(δ^-1)√(N)), which introduces a costly dependence on the Markov chain size N, not present in the classical case.  ...  Appendix B: Szegedy quantum walk Here we review the basics of Szegedy quantum walks. For further details see [29, 42] and references therein. a.  ... 
arXiv:1503.01334v3 fatcat:yuewxj6mqndkxopnvh2qylsnk4


Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, Benoît Valiron
2013 Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13  
Quipper has been used to program a diverse set of nontrivial quantum algorithms, and is able to generate quantum gate representations using trillions of gates.  ...  It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware.  ...  Many quantum algorithms require a circuit to be reversed in the middle of a computation, perhaps within a nested subroutine.  ... 
doi:10.1145/2491956.2462177 dblp:conf/pldi/GreenLRSV13 fatcat:yu7oilhv2rgklelmg6wvsfrs74

Optimal Merging in Quantum k-xor and k-sum Algorithms [article]

María Naya-Plasencia, André Schrottenloher
2019 IACR Cryptology ePrint Archive  
This framework enables us to give new improved quantum k-xor algorithms for all k and list sizes.  ...  (CRYPTO 2012) improve the memory usage over a simple meet-in-the-middle. In this paper, we study quantum algorithms for the k-xor problem.  ...  Thanks to Leo Fan and Chris Peikert for finding a mistake in the first version of our code.  ... 
dblp:journals/iacr/Naya-PlasenciaS19 fatcat:57fwhsn4qraeff2m6fd64jg26m

Quantum-classical hypothesis tests in macroscopic matter-wave interferometry [article]

Björn Schrinski, Stefan Nimmrichter, Klaus Hornberger
2020 arXiv   pre-print
To this end, we consider a rigorous Bayesian test protocol for a parametrized set of hypothetical modifications of quantum theory, including well-studied spontaneous collapse models, that destroy superpositions  ...  This protocol may serve as a guide for the design of future matter-wave experiments ever closer to truly macroscopic scales.  ...  Xu for providing us with their experimental data. This work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Grant No. 298796255.  ... 
arXiv:2004.03392v1 fatcat:mj2b76n6k5e57kyv5tryci3qky

Walk-Sums, Continued Fractions and Unique Factorisation on Digraphs [article]

P.-L. Giscard and S. J. Thwaite and D. Jaksch
2015 arXiv   pre-print
nesting is a product operation between walks that we define.  ...  A simple path is a walk forbidden to visit any vertex more than once. We obtain an explicit formula giving this continued fraction.  ...  Thwaite acknowledges support from Balliol College, a Clarendon Scholarship, and the Alexander von Humboldt Foundation.  ... 
arXiv:1202.5523v5 fatcat:mqvbjmutg5b4dbijtxvcowkq3e
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