Grover search under localized dephasing

J 2019

Grover search under localized dephasing

REITZNER, Daniel a Mark HILLERY

Základní údaje

Originální název

Grover search under localized dephasing

Autoři

REITZNER, Daniel (703 Slovensko, domácí) a Mark HILLERY (840 Spojené státy)

Vydání

Physical Review A, MD USA, AMERICAN PHYSICAL SOCIETY, 2019, 2469-9926

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.777

Kód RIV

RIV/00216224:14330/19:00108144

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1103/PhysRevA.99.012339

UT WoS

000456481200001

Klíčová slova česky

kvantova informace; kvantové vyhledávání

Klíčová slova anglicky

quantum information; quantum search

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 14. 6. 2022 11:54, RNDr. Pavel Šmerk, Ph.D.

Anotace

V originále

Decoherence in quantum searches, and in the Grover search, in particular, has already been extensively studied, leading very quickly to the loss of the quadratic speedup over the classical case, when searching for some target (marked) element within a set of size N. The noise models used were, however, almost always global. In this paper, we study Grover search under the influence of localized partially dephasing noise of rate p. We find that, in the case when the size k of the affected subspace is much smaller than N and the target is unaffected by the noise, namely when kp << root N, the quadratic speedup is retained. Once these restrictions are not met, the quadratic speedup is lost. If the target is affected by the noise, the noise rate needs to scale as 1/root N to keep the speedup. We also observe an intermediate region, where if k similar to N-mu and the target is unaffected, the speedup seems to obey N-mu, which for mu > 0.5 is worse than the quantum, but better than the classical case. We also put obtained results for quantum searches into perspective of quantum walks and searches on graphs.

Návaznosti

GA16-22211S, projekt VaV

Název: Rényiho entropie v kvantovém zpracování informace

Investor: Grantová agentura ČR, Rényiho entropie v kvantovém zpracování informace

Citovat

REITZNER, Daniel a Mark HILLERY. Grover search under localized dephasing. Physical Review A. MD USA: AMERICAN PHYSICAL SOCIETY, 2019, roč. 99, č. 1, s. "012339-1"-"012339-13", 13 s. ISSN 2469-9926. Dostupné z: https://dx.doi.org/10.1103/PhysRevA.99.012339.

@article{1617939,
   author = {Reitzner, Daniel and Hillery, Mark},
   article_location = {MD USA},
   article_number = {1},
   doi = {http://dx.doi.org/10.1103/PhysRevA.99.012339},
   keywords = {quantum information; quantum search},
   language = {eng},
   issn = {2469-9926},
   journal = {Physical Review A},
   title = {Grover search under localized dephasing},
   url = {http://dx.doi.org/10.1103/PhysRevA.99.012339},
   volume = {99},
   year = {2019}
}

TY  - JOUR
ID  - 1617939
AU  - Reitzner, Daniel - Hillery, Mark
PY  - 2019
TI  - Grover search under localized dephasing
JF  - Physical Review A
VL  - 99
IS  - 1
SP  - "012339-1"-"012339-13"
EP  - "012339-1"-"012339-13"
PB  - AMERICAN PHYSICAL SOCIETY
SN  - 24699926
KW  - quantum information
KW  - quantum search
UR  - http://dx.doi.org/10.1103/PhysRevA.99.012339
L2  - http://dx.doi.org/10.1103/PhysRevA.99.012339
N2  - Decoherence in quantum searches, and in the Grover search, in particular, has already been extensively studied, leading very quickly to the loss of the quadratic speedup over the classical case, when searching for some target (marked) element within a set of size N. The noise models used were, however, almost always global. In this paper, we study Grover search under the influence of localized partially dephasing noise of rate p. We find that, in the case when the size k of the affected subspace is much smaller than N and the target is unaffected by the noise, namely when kp << root N, the quadratic speedup is retained. Once these restrictions are not met, the quadratic speedup is lost. If the target is affected by the noise, the noise rate needs to scale as 1/root N to keep the speedup. We also observe an intermediate region, where if k similar to N-mu and the target is unaffected, the speedup seems to obey N-mu, which for mu > 0.5 is worse than the quantum, but better than the classical case. We also put obtained results for quantum searches into perspective of quantum walks and searches on graphs.
ER  -

REITZNER, Daniel a Mark HILLERY. Grover search under localized dephasing. \textit{Physical Review A}. MD USA: AMERICAN PHYSICAL SOCIETY, 2019, roč.~99, č.~1, s.~''012339-1''-''012339-13'', 13 s. ISSN~2469-9926. Dostupné z: https://dx.doi.org/10.1103/PhysRevA.99.012339.

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