### 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 Δt^{2} 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.

Language | English |
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Article number | 105301 |

Pages | 1-17 |

Number of pages | 17 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 10 |

DOIs | |

Publication status | Published - 19 Feb 2014 |

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*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 10, 105301, pp. 1-17. https://doi.org/10.1088/1751-8113/47/10/105301

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

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - High-order quantum algorithm for solving linear differential equations

AU - Berry, Dominic W.

PY - 2014/2/19

Y1 - 2014/2/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84894849729&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/10/105301

DO - 10.1088/1751-8113/47/10/105301

M3 - Article

VL - 47

SP - 1

EP - 17

JO - Journal of Physics A: Mathematical and Theoretical

T2 - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

M1 - 105301

ER -