High-order quantum algorithm for solving linear differential equations

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution.

LanguageEnglish
Article number105301
Pages1-17
Number of pages17
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number10
DOIs
Publication statusPublished - 19 Feb 2014

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Quantum Algorithms
Linear differential equation
Differential equations
differential equations
Higher Order
Quantum computers
Quantum Computer
quantum computers
High-order Methods
Quantum State
Quantum Systems
High Power
engineering
Scaling
Engineering
scaling
Simulation
simulation

Cite this

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High-order quantum algorithm for solving linear differential equations. / Berry, Dominic W.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 10, 105301, 19.02.2014, p. 1-17.

Research output: Contribution to journalArticleResearchpeer-review

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