Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations

摘要

We present two new quantum algorithms. Our first algorithm is ageneralization of amplitude amplification to the case when parts of the quantumalgorithm that is being amplified stop at different times. Our second algorithm uses the first algorithm to improve the running time ofHarrow et al. algorithm for solving systems of linear equations from O(kappa^2log N) to O(kappa log^3 kappa log N) where \kappa is the condition number ofthe system of equations.