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» Quantum Computation and Lattice Problems
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FOCS
1998
IEEE
13 years 12 months ago
The Shortest Vector in a Lattice is Hard to Approximate to Within Some Constant
We show that approximating the shortest vector problem (in any p norm) to within any constant factor less than p 2 is hard for NP under reverse unfaithful random reductions with i...
Daniele Micciancio
STACS
2009
Springer
14 years 2 months ago
Generating Shorter Bases for Hard Random Lattices
We revisit the problem of generating a “hard” random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptogr...
Joël Alwen, Chris Peikert
AICOM
2004
80views more  AICOM 2004»
13 years 7 months ago
A Generic, Collaborative Framework for Interval Constraint Solving
The paper abstracts the contents of a PhD dissertation entitled A Generic, Collaborative Framework for Interval Constraint Solving which has been recently defended. This thesis pre...
Antonio J. Fernández
STOC
2001
ACM
122views Algorithms» more  STOC 2001»
14 years 8 months ago
One-dimensional quantum walks
In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absor...
Andris Ambainis, Eric Bach, Ashwin Nayak, Ashvin V...
FOCS
2003
IEEE
14 years 1 months ago
Quantum Search of Spatial Regions
: Can Grover’s algorithm speed up search of a physical region—for example a 2-D grid of size √ n × √ n? The problem is that √ n time seems to be needed for each query, j...
Scott Aaronson, Andris Ambainis