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- Publications
- Influence

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), we… Expand

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 quantum… Expand

Quantum walks on graphs

- D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani
- Computer Science, Mathematics
- STOC '01
- 18 December 2000

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

One-dimensional quantum walks

- A. Ambainis, E. Bach, Ashwin Nayak, A. Vishwanath, J. Watrous
- Mathematics, Computer Science
- STOC '01
- 6 July 2001

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 the… Expand

Coins make quantum walks faster

- A. Ambainis, J. Kempe, Alexander Rivosh
- Computer Science, Physics
- SODA '05
- 16 February 2004

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 a… Expand

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 probability… Expand

Two-way finite automata with quantum and classical state

- A. Ambainis, J. Watrous
- Computer Science, Mathematics
- Theor. Comput. Sci.
- 16 November 1999

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 unrestricted… Expand

Quantum search of spatial regions

- S. Aaronson, A. Ambainis
- Mathematics, Physics
- 44th Annual IEEE Symposium on Foundations of…
- 9 March 2003

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 for… Expand

Upper Bound on Communication Complexity of Private Information Retrieval

- A. Ambainis
- Computer Science
- ICALP
- 7 July 1997

We construct a scheme for private information retrieval with k databases and communication complexity O(n 1/(2k−1) ).

Private quantum channels

- A. Ambainis, M. Mosca, A. Tapp, R. Wolf
- Computer Science
- Proceedings 41st Annual Symposium on Foundations…
- 12 November 2000

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, we… Expand