6533b82ffe1ef96bd1294707

RESEARCH PRODUCT

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

Andris Ambainis

subject

FOS: Computer and information sciencesMathematics::LogicQuantum PhysicsComputer Science - Computational ComplexityComputer Science - Data Structures and AlgorithmsFOS: Physical sciencesData Structures and Algorithms (cs.DS)Computational Complexity (cs.CC)Quantum Physics (quant-ph)

description

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

yearjournalcountryeditionlanguage
2010-10-21
https://dx.doi.org/10.48550/arxiv.1010.4458