Improve by Alexey

Sorry for the delay, I needed to take a break in order to think and take
a look from another point of view but unfortunately, it did not help so
much. Marek and Iliya, thanks for your comments. Actually, I didn't want
you to send us the definitions, references, and other information from
Wikipedia which I know and understand not worse than you but wanted some
explanation why it is better in comparison with the previous version. As
for section 2 A, basically I prefer the simpler adjusting rule from the
previous version but if everybody prefers the variant from Wikipedia I
am ok with that and updated the section in the appropriate way. As for
section 2 B, we need to decide what two-qubit gate we put on the paper
(control phase gate or the controlled rotation). An advantage of
controlled rotation is a lack of the phase coefficient and a
disadvantage is that it is very similar to the control gate from the
Trugenberger paper (less innovation). Also, the control phase gate may
have benefits at scaling to larger registers due to that in the case
architecture can be more distributed and not everything concentrated on
the ancillary qubit. For the current number of qubits in registers both
the schemes works approximately the same (Iliya, thanks for checking).
I prefer the previous version with the control phase rotation gate but
if everybody prefers the version with CZ it is ok with me. Please,
everybody, let me know what do you think?

Here is an updated version with the CZ gate.

Also, I am still thinking about the title, I like that it is short but
it looks a bit more general then it is needed in my opinion and does not
cover generalization of SOFM to the quantum case. Maybe it would be
better something like "Quantum-assisted unsupervised data clustering on
the basis of Self-Organizing Feature Map"? What do you think?

Here is an updated version of the manuscript. First of all, I returned
to the controlled phase gate version because it looks for me a bit more
original and also may have some advantages for bigger registers. Also, I
tried to reply to all your comments and made modifications in accordance
with them (my comments in the pdf comments file). Looking forward to
your comments.

Author: Ilia Lazarev

bibliography.bib

@@ -1,6 +1,5 @@
-% Encoding: UTF-8
+% Encoding: UTF-8
 
-@comment{jabref-meta: databaseType:bibtex;}
 
 @article{akshay2020,
  author = {V. Akshay and H. Philathong and M.{\hspace{0.167em}}E.{\hspace{0.167em}}S. Morales and J.{\hspace{0.167em}}D. Biamonte},
@@ -782,19 +781,19 @@ @article{purushothaman1997
  volume = {8},
  year = {1997}
 }
-
-@article{pyrkov2019,
- author = {Alexey N. Pyrkov and Tim Byrnes and Valentin V. Cherny},
- doi = {10.3390/sym12010024},
- journal = {Symmetry},
- month = {dec},
- number = {1},
- pages = {24},
- publisher = {{MDPI} {AG}},
- title = {Solitonic Fixed Point Attractors in the Complex Ginzburg{\textendash}Landau Equation for Associative Memories},
- volume = {12},
- year = {2019}
-}
+
+@Article{pyrkov2019,
+  author    = {Alexey N. Pyrkov and Tim Byrnes and Valentin V. Cherny},
+  title     = {Solitonic Fixed Point Attractors in the Complex Ginzburg{\textendash}Landau Equation for Associative Memories},
+  journal   = {Symmetry},
+  year      = {2020},
+  volume    = {12},
+  number    = {1},
+  pages     = {24},
+  month     = {dec},
+  doi       = {10.3390/sym12010024},
+  publisher = {{MDPI} {AG}},
+}
 
 @misc{qiskit,
  author = {H{\'e}ctor Abraham and AduOffei and Ismail Yunus Akhalwaya and Gadi Aleksandrowicz and Thomas Alexander and Gadi Alexandrowics and Eli Arbel and Abraham Asfaw and Carlos Azaustre and AzizNgoueya and Panagiotis Barkoutsos and George Barron and Luciano Bello and Yael Ben-Haim and Daniel Bevenius and Lev S. Bishop and Sorin Bolos and Samuel Bosch and Sergey Bravyi and David Bucher and Artemiy Burov and Fran Cabrera and Padraic Calpin and Lauren Capelluto and Jorge Carballo and Gin{\'e}s Carrascal and Adrian Chen and Chun-Fu Chen and Richard Chen and Jerry M. Chow and Christian Claus and Christian Clauss and Abigail J. Cross and Andrew W. Cross and Simon Cross and Juan Cruz-Benito and Chris Culver and Antonio D. C{\'o}rcoles-Gonzales and Sean Dague and Tareq El Dandachi and Matthieu Dartiailh and DavideFrr and Abd{\'o}n Rodr{\'\i}guez Davila and Anton Dekusar and Delton Ding and Jun Doi and Eric Drechsler and Drew and Eugene Dumitrescu and Karel Dumon and Ivan Duran and Kareem EL-Safty and Eric Eastman and Pieter Eendebak and Daniel Egger and Mark Everitt and Paco Mart{\'\i}n Fern{\'a}ndez and Axel Hern{\'a}ndez Ferrera and Albert Frisch and Andreas Fuhrer and MELVIN GEORGE and Julien Gacon and Gadi and Borja Godoy Gago and Claudio Gambella and Jay M. Gambetta and Adhisha Gammanpila and Luis Garcia and Shelly Garion and Austin Gilliam and Juan Gomez-Mosquera and Salvador de la Puente Gonz{\'a}lez and Jesse Gorzinski and Ian Gould and Donny Greenberg and Dmitry Grinko and Wen Guan and John A. Gunnels and Mikael Haglund and Isabel Haide and Ikko Hamamura and Vojtech Havlicek and Joe Hellmers and {\L}ukasz Herok and Stefan Hillmich and Hiroshi Horii and Connor Howington and Shaohan Hu and Wei Hu and Haruki Imai and Takashi Imamichi and Kazuaki Ishizaki and Raban Iten and Toshinari Itoko and JamesSeaward and Ali Javadi and Ali Javadi-Abhari and Jessica and Kiran Johns and Tal Kachmann and Naoki Kanazawa and Kang-Bae and Anton Karazeev and Paul Kassebaum and Spencer King and Knabberjoe and Arseny Kovyrshin and Rajiv Krishnakumar and Vivek Krishnan and Kevin Krsulich and Gawel Kus and Ryan LaRose and Rapha{\"e}l Lambert and Joe Latone and Scott Lawrence and Dennis Liu and Peng Liu and Yunho Maeng and Aleksei Malyshev and Jakub Marecek and Manoel Marques and Dolph Mathews and Atsushi Matsuo and Douglas T. McClure and Cameron McGarry and David McKay and Dan McPherson and Srujan Meesala and Martin Mevissen and Antonio Mezzacapo and Rohit Midha and Zlatko Minev and Abby Mitchell and Nikolaj Moll and Michael Duane Mooring and Renier Morales and Niall Moran and MrF and Prakash Murali and Jan M{\"u}ggenburg and David Nadlinger and Ken Nakanishi and Giacomo Nannicini and Paul Nation and Edwin Navarro and Yehuda Naveh and Scott Wyman Neagle and Patrick Neuweiler and Pradeep Niroula and Hassi Norlen and Lee James O'Riordan and Oluwatobi Ogunbayo and Pauline Ollitrault and Steven Oud and Dan Padilha and Hanhee Paik and Simone Perriello and Anna Phan and Francesco Piro and Marco Pistoia and Alejandro Pozas-iKerstjens and Viktor Prutyanov and Daniel Puzzuoli and Jes{\'u}s P{\'e}rez and Quintiii and Rudy Raymond and Rafael Mart{\'\i}n-Cuevas Redondo and Max Reuter and Julia Rice and Diego M. Rodr{\'\i}guez and RohithKarur and Max Rossmannek and Mingi Ryu and Tharrmashastha SAPV and SamFerracin and Martin Sandberg and Hayk Sargsyan and Ninad Sathaye and Bruno Schmitt and Chris Schnabel and Zachary Schoenfeld and Travis L. Scholten and Eddie Schoute and Joachim Schwarm and Ismael Faro Sertage and Kanav Setia and Nathan Shammah and Yunong Shi and Adenilton Silva and Andrea Simonetto and Nick Singstock and Yukio Siraichi and Iskandar Sitdikov and Seyon Sivarajah and Magnus Berg Sletfjerding and John A. Smolin and Mathias Soeken and Igor Olegovich Sokolov and SooluThomas and Dominik Steenken and Matt Stypulkoski and Jack Suen and Shaojun Sun and Kevin J. Sung and Hitomi Takahashi and Ivano Tavernelli and Charles Taylor and Pete Taylour and Soolu Thomas and Mathieu Tillet and Maddy Tod and Enrique de la Torre and Kenso Trabing and Matthew Treinish and TrishaPe and Wes Turner and Yotam Vaknin and Carmen Recio Valcarce and Francois Varchon and Almudena Carrera Vazquez and Desiree Vogt-Lee and Christophe Vuillot and James Weaver and Rafal Wieczorek and Jonathan A. Wildstrom and Robert Wille and Erick Winston and Jack J. Woehr and Stefan Woerner and Ryan Woo and Christopher J. Wood and Ryan Wood and Stephen Wood and Steve Wood and James Wootton and Daniyar Yeralin and Richard Young and Jessie Yu and Christopher Zachow and Laura Zdanski and Christa Zoufal and Zoufalc and a-matsuo and adekusar-drl and azulehner and bcamorrison and brandhsn and chlorophyll-zz and dan1pal and dime10 and drholmie and elfrocampeador and faisaldebouni and fanizzamarco and gadial and gruu and jliu45 and kanejess and klinvill and kurarrr and lerongil and ma5x and merav-aharoni and michelle4654 and ordmoj and sethmerkel and strickroman and sumitpuri and tigerjack and toural and vvilpas and welien and willhbang and yang.luh and yelojakit and yotamvakninibm},
@@ -1125,4 +1124,5 @@ @article{zhu2018
  volume = {10},
  year = {2018}
 }
-
+
+@Comment{jabref-meta: databaseType:bibtex;}