• Publications
  • Influence
Quantum walk algorithm for element distinctness
  • A. Ambainis
  • Mathematics, Physics
  • 45th Annual IEEE Symposium on Foundations of…
  • 31 October 2003
TLDR
We use quantum walks to construct a new quantum algorithm for element distinctness (the problem of finding two equal items among N given items). Expand
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  • 63
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Quantum lower bounds by quantum arguments
  • A. Ambainis
  • Mathematics, Computer Science
  • STOC '00
  • 23 February 2000
TLDR
We propose a new method for proving lower bounds on quantum query algorithms. Expand
  • 387
  • 57
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Quantum walks on graphs
TLDR
We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Expand
  • 518
  • 39
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One-dimensional quantum walks
TLDR
We define and analyze quantum computational variants of random walks on one-dimensional lattices, including the Hadamard walk, a quantum analog of the symmetric random walk. Expand
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Coins make quantum walks faster
TLDR
We show how to search a grid of <i>N</i> items arranged on a √ × √<N> grid in discrete time using a discrete time quantum walk, using a coin-flip operation, and give several extensions of quantum walk search algorithms and generic expressions for its performance. Expand
  • 251
  • 34
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1-way quantum finite automata: strengths, weaknesses and generalizations
  • A. Ambainis, R. Freivalds
  • Computer Science, Physics
  • Proceedings 39th Annual Symposium on Foundations…
  • 24 February 1998
We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probabilityExpand
  • 253
  • 28
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Quantum search of spatial regions
  • S. Aaronson, A. Ambainis
  • Mathematics, Computer Science
  • 44th Annual IEEE Symposium on Foundations of…
  • 9 March 2003
TLDR
A model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Expand
  • 195
  • 25
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Two-way finite automata with quantum and classical state
TLDR
We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-qfa) model which may be simpler to implement than unrestricted 2qfa's. Expand
  • 119
  • 23
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Upper Bound on Communication Complexity of Private Information Retrieval
TLDR
We construct a scheme for private information retrieval with k databases and communication complexity O(n 1/(2k−1) . Expand
  • 189
  • 18
Private quantum channels
TLDR
We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. Expand
  • 198
  • 18
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