• Publications
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Quantum walk algorithm for element distinctness
  • A. Ambainis
  • Computer Science, Physics
  • 45th Annual IEEE Symposium on Foundations of…
  • 31 October 2003
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), weExpand
  • 593
  • 64
Quantum lower bounds by quantum arguments
  • A. Ambainis
  • Computer Science, Mathematics
  • STOC '00
  • 23 February 2000
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with on input and then modifies the input, we use a quantumExpand
  • 368
  • 56
Quantum walks on graphs
We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution,Expand
  • 487
  • 39
One-dimensional quantum walks
We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call theExpand
  • 416
  • 33
Coins make quantum walks faster
We show how to search <i>N</i> items arranged on a √<i>N</i> × √<i>N</i> grid in time <i>O</i>(√<i>N</i> log <i>N</i>), using a discrete time quantum walk. This result for the first time exhibits aExpand
  • 237
  • 33
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
  • 249
  • 28
Two-way finite automata with quantum and classical state
We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestrictedExpand
  • 128
  • 28
Quantum search of spatial regions
Can Grover's quantum search algorithm speed up search of a physical region - for example a 2D grid of size /spl radic/n x /spl radic/n? The problem is that /spl radic/n time seems to be needed forExpand
  • 187
  • 25
Upper Bound on Communication Complexity of Private Information Retrieval
We construct a scheme for private information retrieval with k databases and communication complexity O(n 1/(2k−1) ).
  • 186
  • 21
Private quantum channels
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. In particular, weExpand
  • 181
  • 17