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Kvantu klejošana un pielietojumi

Projekta nosaukums:  Kvantu klejošana un pielietojumi
Projekta līguma numurs: 1.1.1.2/VIAA/1/16/002
Projekta sadarbības partneri: Prof. Renato Portugal (National Laboratory for Scientific Computing - LNCC, Petrópolis, Brazil)
Projekta īstenošanas termiņš: 01.11.2017 - 31.10.2020
Projekta kopējais finansējums, LU daļa: 133806.00 EUR, LU daļa 6690.30 EUR 
Projekta mērķis: Mēs plānojam risināt svarīgus, zinātniskus problēmjautājumus un izpētīt jaunas pieejas, izmantojot kvantu klejošanu. Mēs izpētīsim meklēšanu ar kvantu klejošanu dažādās vidē, analizēsim to izturēšanos dekoherences klātbūtnē, un iegūsim jaunas atziņas par pielietojumiem, kas ir saistīti ar kvantu tīkliem.
Projekta rezultāti: 5 publikācijas

During the period from November, 2017 to April, 2018:

The main problems adressed during this period are: decoherence on the staggered quantum walk model; analysis of the staggered quantum walk on the 8-4-clique graph; and quantum search with partial measurements. These problems are inserted in the first working package of the research project.
Posters were presented at the 21th Annual Conference on Quantum Information Processing (QIP-2018 https://qutech.nl/qip2018/) held in Delft, Netherlands, on January, 2018:

During the period from May, 2018 to July, 2018:
We continue to work on the problems mentioned before.Visit to our partner National Laboratory for Scientific Computing (http://www.lncc.br/) in Petrópolis, Brazil (from 21.05 to 31.05 and from 11.06 to 18.06):  we collaborate with the Quantum Computing Group (http://qubit.lncc.br/). Scientific discussions were established with Prof. Renato Portugal and also with Prof. Franklin Marquezino from the Federal University of Rio de Janeiro.

During the period from Aug, 2018 to Oct, 2018:
Attended the conference "Modern Topics in Quantum Information" held in Natal, Brazil, from 30th July 30 to 17th Aug. I was able to attend the last two weeks. One week was the "Modern Topics in Quantum Information Conference" with invited talks from experts in the area. The other week happened the "Convexity and quantum information workshop" with invited talks and discussions between the participants.The paper "On the probability of finding marked connected components using quantum walks" (https://arxiv.org/abs/1710.04046) is now published on Lobachevskii Journal of Mathematics, 2018, Vol. 39, No. 7, pp. 1016–1023 (https://doi.org/10.1134/S1995080218070144).- New manuscript uploaded: "The role of tessellation intersection in staggered quantum walks" (https://arxiv.org/abs/1810.02387)

During the period from Feb, 2019 to Aug, 2020:

Two papers are now published:

  •  Nahimovs, N., Santos, R.A.M. & Khadiev, K.R. Adjacent Vertices Can be Hard to Find by Quantum Walks. Moscow University Computational Mathematics and Cybernetics 43, 32–39 (2019). doi.org/10.3103/S0278641919010060
  • Santos, R.A.M. The role of tessellation intersection in staggered quantum walks. Natural Computing (2019). doi.org/10.1007/s11047-019-09758-2

Review on the literature has been done. Worked on some simulations of Szegedy’s quantum walk on bipartite graphs and studied about lamplighter random walks and how would be its quantum version on the complete graph.

During the period from Sept, 2020 to Nov, 2020:

We have reinitiated collaboration with our partner from LNCC. Together with Renato Portugal and Gustavo Bezerra we are discussing the problem about quantum walk counting. Currently, reviewing some works in the literature.

Simulations have been done for the decoherence problem on staggered quantum walks in collaboration with Franklin Marquezino. The idea is to use the results presented in the published paper “The role of tessellation intersection in staggered quantum walks”.

About the lamplighter quantum walk problem: we can show that the lamplighter random walk on the complete graph can be modelled as a staggered quantum walk on the hypercube. Also we have found out there already exists a model in the literature called “interacting quantum walks” which seems to be a natural quantization of the lamplighter random walks.

In collaboration with Nikolajs Nahimovs, we are working on the problem of searching multiple marked vertices with lackadaisical quantum walks on different types of grids. Some simulations have been done.

 

During the period from Dec, 2020 to Feb, 2021:

We continue to work on the following problems: Searching multiple marked vertices with lackadaisical quantum walks on different types of grids in collaboration with Nikolajs Nahimovs; Quantum walks counting in collaboration with Renato Portugal and Gustavo Bezerra; Decoherence on staggered quantum walks in collaboration with Franklin Marquezino; The lamplighter random walk on the complete graph.

Participation in the QIP conference held on-line in January 2021, with presentation of the poster:

During the period from Mar, 2021 to May, 2021:

We continue to work on the following problems: Quantum walks counting in collaboration with Renato Portugal and Gustavo Bezerra; Decoherence on staggered quantum walks in collaboration with Franklin Marquezino; Searching multiple marked vertices with lackadaisical quantum walks on different types of grids in collaboration with Nikolajs Nahimovs (manuscript is on arxiv); State transfer on the complete bipartite graph.

During the period from Jun, 2021 to Aug, 2021:

Participation in TQC 2021 conference (https://tqc2021.lu.lv/) held on-line in July.

We have been working on the manuscript  “Lackadaisical quantum walks on 2D grids with multiple marked vertices” in collaboration with Nikolajs Nahimovs. It is now accepted for publication in the Journal of Physics A: Mathematical and Theoretical (https://doi.org/10.1088/1751-8121/ac21e3 ).

We continue to work on the following problems: Quantum walks counting in collaboration with Renato Portugal and Gustavo Bezerra – a quantum algorithm for a particular case has been obtained; Decoherence on staggered quantum walks in collaboration with Franklin Marquezino – we have started writing a manuscript and we are running some necessary simulations; State transfer on the complete bipartite graph – simulations and spectrum calculations have been done.

During the period from Oct, 2021 to Nov, 2021:

We continue to work on the following problems:

  • Decoherence on staggered quantum walks in collaboration with Franklin Marquezino – we have finished writing the first manuscript. It is now available in arxiv (Decoherence on staggered quantum walks) and we are preparing the final version to submit to a journal;
  • State transfer on the complete bipartite graph – we have tried to find the spectrum of the evolution operator from the lackadaisical quantum walk. Simulations and finalization of the quantum state transfer algorithm have been done. We have finished writing the first manuscript. It is now available in arxiv (Quantum state transfer on the complete bipartite graph) and submitted to a journal;
  • Quantum walks counting in collaboration with Renato Portugal and Gustavo Bezerra –  we have been calculating the eigenvalues and eigenvectors of the evolution operator to use in the algorithm.

During the period from Dec, 2021 to Feb, 2022:

We have worked on the revision of the following papers that are now published:

 
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