Search and state transfer between hubs by quantum walks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00376730" target="_blank" >RIV/68407700:21340/24:00376730 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1103/PhysRevA.110.022422" target="_blank" >https://doi.org/10.1103/PhysRevA.110.022422</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevA.110.022422" target="_blank" >10.1103/PhysRevA.110.022422</a>

Result language

angličtina

Original language name

Search and state transfer between hubs by quantum walks

Original language description

Search and state transfer between hubs, i.e., fully connected vertices, on otherwise arbitrary connected graph is investigated. Motivated by a recent result of Razzoli et al. [J. Phys. A: Math. Theor. 55, 265303 (2022)] on the universality of hubs in continuous-time quantum walks and spatial search, we extend the investigation to state transfer and also to the discrete-time case. We show that the continuous-time quantum walk allows for perfect state transfer between multiple hubs if the numbers of senders and receivers are close. Turning to the discrete-time case, we show that the search for hubs is successful provided that the initial state is locally modified to account for a degree of each individual vertex. Concerning state transfer using discrete-time quantum walk, it is shown that between a single sender and a single receiver one can transfer two orthogonal states in the same run time. Hence, it is possible to transfer an arbitrary quantum state of a qubit between two hubs. In addition, if the sender and the receiver know each other location, another linearly independent state can be transferred, allowing for exchange of a qutrit state. Finally, we consider the case of transfer between multiple senders and receivers. In this case we cannot transfer specific quantum states. Nevertheless, quantum walker can be transferred with high probability in two regimes-either when there is a similar number of senders and receivers, which is the same as for the continuous-time quantum walk, or when the number of receivers is considerably larger than the number of senders. Our investigation is based on dimensional reduction utilizing the invariant subspaces of the respective evolutions and the fact that for the appropriate choice of the loop weights the problem can be reduced to the complete graph with loops.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

<a href="/en/project/GA23-07169S" target="_blank" >GA23-07169S: Multipartite quantum dynamics on graphs and hypergraphs – theory and applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2024

Confidentiality

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

Name of the periodical

PHYSICAL REVIEW A

ISSN

2469-9926

e-ISSN

2469-9934

Volume of the periodical

110

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

17

Pages from-to

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UT code for WoS article

001295424200006

EID of the result in the Scopus database

2-s2.0-85201222182