Preconditioned quantum linear system algorithm

We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used t...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Clader, B D, Jacobs, B C, Sprouse, C R
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 07.05.2013
Subjects:	Algorithms Electromagnetic scattering Linear systems Scattering cross sections Solvers
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1301.2340