Filters








2,329 Hits in 7.0 sec

Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection [article]

Kaspars Balodis, Jānis Iraids
2015 arXiv   pre-print
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model  ...  For both of these problems the known lower bounds are trivial (Ω(√(n)) and Ω(n), respectively) and there is no known matching upper bound.  ...  Setting f = OR and g = Graph-Collision G gives the desired bound. As the next corollary shows, a better lower bound on Graph-Collision implies a better lower bound on the Triangle problem.  ... 
arXiv:1507.03885v1 fatcat:m7gwpzsbcnc5rbsbvjd4dlag3i

Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection

Kaspars Balodis, Jānis Iraids
2016 Baltic Journal of Modern Computing  
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model  ...  For both of these problems the known lower bounds are trivial (Ω( √ n) and Ω(n), respectively) and there is no known matching upper bound.  ...  Setting f = OR and g = GRAPH-COLLISION G gives the desired bound. As the next corollary shows, a better lower bound on GRAPH-COLLISION implies a better lower bound on the TRIANGLE problem.  ... 
doi:10.22364/bjmc.2016.4.4.10 fatcat:xwe77rfkbncmvckbfzc55zk4am

On the Power of Non-adaptive Learning Graphs

Aleksandrs Belovs, Ansis Rosmanis
2013 2013 IEEE Conference on Computational Complexity  
This also gives a quantum query lower bound for the triangle sum problem.  ...  The construction is based on orthogonal arrays and generalizes the quantum query lower bound for the k-sum problem derived recently by Belovs andŠpalek (Proceeding of 4th ACM ITCS, 323-328, 2012).  ...  Acknowledgements A.B. would like to thank Troy Lee, Robin Kothari and Rajat Mittal for sharing their ideas on the limitations of learning graphs.  ... 
doi:10.1109/ccc.2013.14 dblp:conf/coco/BelovsR13 fatcat:wzeax7k42jfqnesi2nbnr65seq

A quantum query algorithm for the graph collision problem [article]

Dmitry Gavinsky, Tsuyoshi Ito
2012 arXiv   pre-print
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G.  ...  up to the sqrt(log n) factor on most graphs.  ...  Acknowledgments Dmitry Gavinsky is grateful to Ryan O'Donnell, Rocco Servedio, Srikanth Srinivasan and Li-Yang Tan for helpful discussions.  ... 
arXiv:1204.1527v1 fatcat:o44qph5yrvdx7pagl35ivsirnu

On the Power of Non-adaptive Learning Graphs

Aleksandrs Belovs, Ansis Rosmanis
2014 Computational Complexity  
This also gives a quantum query lower bound for the triangle sum problem.  ...  The construction is based on orthogonal arrays and generalizes the quantum query lower bound for the k-sum problem derived recently by Belovs and Špalek (Proceeding of 4th ACM ITCS, 323-328, 2012).  ...  Acknowledgements A.B. would like to thank Troy Lee, Robin Kothari and Rajat Mittal for sharing their ideas on the limitations of learning graphs.  ... 
doi:10.1007/s00037-014-0084-1 fatcat:3a2lurou7nhd5ilcvv6dxakd4y

On the Power of Non-Adaptive Learning Graphs [article]

Aleksandrs Belovs, Ansis Rosmanis
2012 arXiv   pre-print
This also gives a quantum query lower bound for the triangle-sum problem.  ...  The construction is based on orthogonal arrays, and generalizes the quantum query lower bound for the k-sum problem derived recently in arXiv:1206.6528.  ...  Acknowledgments A.B. would like to thank Troy Lee, Robin Kothari and Rajat Mittal for sharing their ideas on the limitations of learning graphs.  ... 
arXiv:1210.3279v2 fatcat:dnoyeb5stfaa5ok575jjjo4dvi

Adversary Lower Bound for the k-sum Problem [article]

Aleksandrs Belovs, Robert Spalek
2012 arXiv   pre-print
We prove a tight quantum query lower bound Ω(n^k/(k+1)) for the problem of deciding whether there exist k numbers among n that sum up to a prescribed number, provided that the alphabet size is sufficiently  ...  We are grateful to Kassem Kalach for informing about the applications of the k-sum problem in Merkle puzzles, and for reporting on some minor errors in the early version of the paper.  ...  Acknowledgments A.B. would like to thank Andris Ambainis, Troy Lee and Ansis Rosmanis for valuable discussions.  ... 
arXiv:1206.6528v2 fatcat:epzhatctw5hmhdrrekebgdcfsi

New Results on Quantum Property Testing

Sourav Chakraborty, Eldar Fischer, Arie Matsliah, Ronald De Wolf, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
, based on Shor's algorithm and a modification of a classical lower bound by Lachish and Newman [27] .  ...  Based on this result, we also reduce the query complexity of graph isomorphism testers with quantum oracle access.  ...  for pointing out that his Fourier checking result in [1] was the first constant-vs-polynomial quantum speed-up in property testing.  ... 
doi:10.4230/lipics.fsttcs.2010.145 dblp:conf/fsttcs/ChakrabortyFMW10 fatcat:vwmxfq2oxvcu7bp3gkzlqy5wvu

Quantum Algorithm for Commutativity Testing of a Matrix Set [article]

Yuki Kelly Itakura
2005 arXiv   pre-print
We also present Ambainis's method of lower bounding technique (quant-ph/0002066) to obtain a lower bound for this problem.  ...  We give an O(k^4/5n^9/5) algorithm as well as a lower bound of Omega(k^1/2n). We generalize the technique used in coming up with the upper bound to solve a broader range of similar problems.  ...  Acknowledgements The author would like to acknowledge Ashwin Nayak for supervion, Richard Cleve for reading this essay, Andris Ambainis and Frederic Magniez for consultation on lower bounds and the differences  ... 
arXiv:quant-ph/0509206v1 fatcat:d2vtqjggnrdgtbflzrke6rpmqa

New Results on Quantum Property Testing [article]

Sourav Chakraborty, Eldar Fischer, Arie Matsliah, Ronald de Wolf
2010 arXiv   pre-print
, based on Shor's algorithm and a modification of a classical lower bound by Lachish and Newman lachish&newman:periodicity.  ...  Based on this result, we also reduce the query complexity of graph isomorphism testers with quantum oracle access.  ...  result in [1] was the first constant-vs-polynomial quantum speed-up in property testing.  ... 
arXiv:1005.0523v3 fatcat:2ceczft5bvhmdfdvaujqhfktwq

Applications of the Adversary Method in Quantum Query Algorithms [article]

Aleksandrs Belovs
2014 arXiv   pre-print
Our results are as follows: * We develop a new technique for the construction of quantum algorithms: learning graphs. * We use learning graphs to improve quantum query complexity of the triangle detection  ...  and the k-distinctness problems. * We prove tight lower bounds for the k-sum and the triangle sum problems. * We construct quantum algorithms for some subgraph-finding problems that are optimal in terms  ...  Lower Bounds for Quantum Query Complexity In this chapter, we describe some known techniques for proving lower bounds on quantum query complexity.  ... 
arXiv:1402.3858v1 fatcat:etcbmdej4bfxbhieqqfq6wd3lq

Quantum Complexity of Testing Group Commutativity [article]

Frederic Magniez, Ashwin Nayak (U. Waterloo and Perimeter Inst.)
2007 arXiv   pre-print
For the lower bound of Omega(k^2/3), we give a reduction from a special case of Element Distinctness to our problem.  ...  We construct a quite optimal quantum algorithm for this problem whose complexity is in O (k^2/3). The algorithm uses and highlights the power of the quantization method of Szegedy.  ...  Then Theorem 2 (due to Aaronson and Shi [AS04] and Kutin [Kut05] , together with Ambainis [Amb05] ) implies the lower bound.  ... 
arXiv:quant-ph/0506265v4 fatcat:sfknwj2apbdrfpamh2u5iis4mm

Adversary Lower Bounds for the Collision and the Set Equality Problems [article]

Aleksandrs Belovs, Ansis Rosmanis
2017 arXiv   pre-print
We prove tight Ω(n^1/3) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough.  ...  In particular, this gives nearly tight lower bounds for the k-Sum and the Triangle-Sum problems.  ...  Note that H Dual Learning Graph Perspective Our lower bounds for the Collision and the Set Equality problems are intrinsicly based on the dual learning graph for these problems developed in [9] .  ... 
arXiv:1310.5185v4 fatcat:iy732z4akvdxjk324sjxfn5us4

Improved Quantum Query Algorithms for Triangle Finding and Associativity Testing [chapter]

Troy Lee, Frédéric Magniez, Miklos Santha
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show that the quantum query complexity of detecting if an n-vertex graph contains a triangle is O(n 9/7 ). This improves the previous best algorithm of Belovs [2] making O(n 35/27 ) queries.  ...  Our algorithms are designed using the learning graph framework of Belovs. We give a family of algorithms for detecting constant-sized subgraphs, which can possibly be directed and colored.  ...  Acknowledgements We would like to thank Aleksandrs Belovs for discussions and comments on an earlier draft of this work.  ... 
doi:10.1137/1.9781611973105.107 dblp:conf/soda/LeeMS13 fatcat:k65v7a5l2rcv5o446odv3n57jq

Improved Quantum Query Algorithms for Triangle Finding and Associativity Testing [article]

Troy Lee and Frederic Magniez and Miklos Santha
2012 arXiv   pre-print
We show that the quantum query complexity of detecting if an n-vertex graph contains a triangle is O(n^9/7). This improves the previous best algorithm of Belovs making O(n^35/27) queries.  ...  Our algorithms are designed using the learning graph framework of Belovs. We give a family of algorithms for detecting constant-sized subgraphs, which can possibly be directed and colored.  ...  Acknowledgements We would like to thank Aleksandrs Belovs for discussions and comments on an earlier draft of this work.  ... 
arXiv:1210.1014v1 fatcat:57t2dmwmm5bbfo3ejdvahgcak4
« Previous Showing results 1 — 15 out of 2,329 results