Quantum algorithm for solving linear systems of equations

Details Quantum algorithm for solving linear systems of equations Quantum algorithm for solving linear systems of equations

2008-11-19

arxiv.org/abs/0811.3171v3

Phys. Rev. Lett. vol. 15, no. 103, pp. 150502 (2009)

Physics

Quantum Physics

15 pages. v2 is much longer, with errors fixed, run-time improved and a new BQP-completeness result added. v3 is the final pub

Scientific paper

10.1103/PhysRevLett.103.150502

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.

Affiliated with

Also associated with

No associations

Rating

Quantum algorithm for solving linear systems of equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum algorithm for solving linear systems of equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum algorithm for solving linear systems of equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-667216