Simulating hamiltonian dynamics with a truncated taylor series

Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, Rolando D. Somma

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

LanguageEnglish
Article number090502
Pages1-5
Number of pages5
JournalPhysical Review Letters
Volume114
Issue number9
DOIs
Publication statusPublished - 3 Mar 2015

Fingerprint

Taylor series
quantum computers
costs
operators

Bibliographical note

Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015). Simulating Hamiltonian dynamics with a truncated Taylor series. Physical review letters, 114(9), 090502. Copyright 2015 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.114.090502.

Cite this

Berry, Dominic W. ; Childs, Andrew M. ; Cleve, Richard ; Kothari, Robin ; Somma, Rolando D. / Simulating hamiltonian dynamics with a truncated taylor series. In: Physical Review Letters. 2015 ; Vol. 114, No. 9. pp. 1-5.
@article{a75d783d403043dfa2e06c77762cb0fc,
title = "Simulating hamiltonian dynamics with a truncated taylor series",
abstract = "We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.",
author = "Berry, {Dominic W.} and Childs, {Andrew M.} and Richard Cleve and Robin Kothari and Somma, {Rolando D.}",
note = "Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015). Simulating Hamiltonian dynamics with a truncated Taylor series. Physical review letters, 114(9), 090502. Copyright 2015 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.114.090502.",
year = "2015",
month = "3",
day = "3",
doi = "10.1103/PhysRevLett.114.090502",
language = "English",
volume = "114",
pages = "1--5",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "9",

}

Simulating hamiltonian dynamics with a truncated taylor series. / Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard; Kothari, Robin; Somma, Rolando D.

In: Physical Review Letters, Vol. 114, No. 9, 090502, 03.03.2015, p. 1-5.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Simulating hamiltonian dynamics with a truncated taylor series

AU - Berry, Dominic W.

AU - Childs, Andrew M.

AU - Cleve, Richard

AU - Kothari, Robin

AU - Somma, Rolando D.

N1 - Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015). Simulating Hamiltonian dynamics with a truncated Taylor series. Physical review letters, 114(9), 090502. Copyright 2015 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.114.090502.

PY - 2015/3/3

Y1 - 2015/3/3

N2 - We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

AB - We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

UR - http://www.scopus.com/inward/record.url?scp=84924352855&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/FT100100761

U2 - 10.1103/PhysRevLett.114.090502

DO - 10.1103/PhysRevLett.114.090502

M3 - Article

VL - 114

SP - 1

EP - 5

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

M1 - 090502

ER -