Entangling and disentangling in Grover's search algorithm

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113867" target="_blank" >RIV/00216224:14330/19:00113867 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.tcs.2018.10.001" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2018.10.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2018.10.001" target="_blank" >10.1016/j.tcs.2018.10.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Entangling and disentangling in Grover's search algorithm

Popis výsledku v původním jazyce

Entanglement is believed to be crucial in making quantum algorithms more powerful than their classical counterparts for certain computational tasks. In Grover's search algorithm, the Grover's operator iteration G can be decomposed into two basic operators, i.e., G = RO, where O is so called the Oracle operator and R is the Reflection operator. To probe the production/depletion of entanglement from basic operator level, we investigate the roles the Oracle and the Reflection operators play in the entanglement dynamics during Grover's search algorithm application. Using geometric measure of entanglement (GME), we show that the Oracle operator is an entangling operator which almost always produces (increases) entanglement while the Reflection operator is a disentangling operator which mainly depletes (decreases) entanglement. We explicitly demonstrate that there exists a turning point during the Grover's iteration application with the following properties. Before that turning point, the entanglement is almost always increased when the Oracle operator is applied, and the effect of the Reflection operator on the level of entanglement can be almost ignored. However, after the turning point, both the Oracle and the Reflection operators play important roles to the entanglement, more exactly, the Reflection operator significantly decreases entanglement while the Oracle operator increases entanglement. All these results are carefully demonstrated.

Název v anglickém jazyce

Entangling and disentangling in Grover's search algorithm

Popis výsledku anglicky

Entanglement is believed to be crucial in making quantum algorithms more powerful than their classical counterparts for certain computational tasks. In Grover's search algorithm, the Grover's operator iteration G can be decomposed into two basic operators, i.e., G = RO, where O is so called the Oracle operator and R is the Reflection operator. To probe the production/depletion of entanglement from basic operator level, we investigate the roles the Oracle and the Reflection operators play in the entanglement dynamics during Grover's search algorithm application. Using geometric measure of entanglement (GME), we show that the Oracle operator is an entangling operator which almost always produces (increases) entanglement while the Reflection operator is a disentangling operator which mainly depletes (decreases) entanglement. We explicitly demonstrate that there exists a turning point during the Grover's iteration application with the following properties. Before that turning point, the entanglement is almost always increased when the Oracle operator is applied, and the effect of the Reflection operator on the level of entanglement can be almost ignored. However, after the turning point, both the Oracle and the Reflection operators play important roles to the entanglement, more exactly, the Reflection operator significantly decreases entanglement while the Oracle operator increases entanglement. All these results are carefully demonstrated.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Svazek periodika

773

Číslo periodika v rámci svazku

14 June 2019

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

138-152

Kód UT WoS článku

000469907500009

EID výsledku v databázi Scopus

2-s2.0-85055153956