#### QES Seminar, 3/29/10: A quantum algorithm for solving linear systems of equations

(More about event)Aram Harrow, University of Bristol

A quantum algorithm for solving linear systems of equations -- Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

**Location:**
Bowen Hall Atrium

**Date/Time: **03/29/10
at
12:30 pm
- 03/25/10
at
01:30 am

**Category: **PRISM/MITRE (QES) Seminar Series

**Department: **PRISM