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News & Views Quantum algorithms: Equation solving by simulation

By Andrew M. Childs


Quantum computers can outperform classical ones at some tasks, but the full scope of their power is unclear. A recent quantum algorithm suggests the possibility of far-reaching applications. Quantum mechanical computers have the potential to quickly perform calculations that are infeasible with current technology. There are fast quantum algorithms to simulate the dynamics of quantum systems 1 and to decompose integers into their prime factors, 2 problems thought to be intractable for classical computers. But quantum computation is not a magic bullet—some problems cannot be solved dramatically faster by quantum computers than by classical ones. So is a quantum computer fundamentally a special-purpose device, suitable only for number-theoretic calculations or problems that are inherently quantum? In a recent article in Physical Review Letters, 3 Aram Harrow, Avinatan Hassidim, and Seth Lloyd describe how quantum computers can extract information about the solutions to linear equations, a fundamental task with broad applications. The basic problem of finding a vector ⃗x satisfying A⃗x = ⃗b for some given matrix A and vector ⃗b arises throughout science and engineering. For example, signal processing, convex optimization, and finite element analysis all rely on solving linear equations. Due to the importance of linear systems, considerable effort has been spent on finding fast algorithms for solving them. One simpl

Year: 2011
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