An Efficient Quantum Algorithm for Lattice Problems Achieving Subexponential Approximation Factor

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United States Simons Institute for the Theory of Computing
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Duration: 1:07:21
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Sean Hallgren (Penn State University & Senior Visitor at Simons Institute 2021-22)
Quantum Colloquium, Sep 21, 2021
https://simons.berkeley.edu/events/efficient-quantum-algorithm-lattice-problems-achieving-subexponential-approximation-factor

We give a polynomial-time quantum algorithm for solving the Bounded Distance Decoding problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm achieves an exponential speedup compared to the best known classical algorithm, and is the first example of an exponential speedup on a general lattice problem not connected to number theory.

Joint work with Lior Eldar.



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Simons Institute
theoretical computer science
UC Berkeley
Computer Science
Theory of Computation
Theory of Computing
Quantum Colloquium