Greetings! This is Bikas. My brief CV is as follows: Born in Dec.
1952, in Calcutta, to Bimal K. Chakrabarti and Pratima Chakrabarti.
Got my Ph. D. Degree from Calcutta
University in 1979. After that, I was postdoctoral fellow at Department
of Theoretical Physics, University of Oxford and then at
Institute for Theoretical Physics, University of Cologne. I joined Saha Institute of Nuclear Physics as faculty in
September 1983, where
I am Emeritus Professor since January 2018.
Married to Mrs. Kaberi Chakrabarti. Have two sons:
Kalyan Sundar Chakrabarti and
Anindya Sundar Chakrabarti.
At present, J. C. Bose National Fellow and Emeritus Professor (Former Professor & Director) at
Saha Institute of Nuclear Physics, Kolkata, Honorary Emeritus Professor at S.N. Bose National Centre for Basic Sciences, Kolkata
and Honorary Visiting Professor of Economics, Indian Statistical Institute, Kolkata.
I have professional interest in
statistical physics, condensed matter physics,
computational physics, and their application to social sciences.
See my papers, reviews or books.
Our ideas on quantum search techniques, together with the researches from a number of other groups, have led to important developments recently. The advantages of quantum tunneling (through steep but narrow effective barriers) in searching for the global solution(s) of NPhard problems (avoiding the innumerable localized ones), shown first by us in 1989 and in the subsequent works on Quantum Annealing have ultimately led to an exciting development of a class of specialpurpose (Analog) Quantum Computers. Some of its remarkably successful versions are now available commercially (e.g. , by DWave Systems) :
In 2015 NASA's Quantum Artificial Intelligence Laboratory installed the DWave 2X having over 1000 qubits, which is understood to be hundred
million times faster for some typical computationally hard jobs
(see also).
: See the (highlighted) last part of the entry "CITATIONS OF OUR WORK INCLUDE" for some typical recent citations in this context.
RESEARCH:
Authored/coauthored more than 180 papers in refereed journals,
7 reviews [1 in Eur. Phys. J. B, 2 in Phys. Rep. &
4 in Rev. Mod. Phys. (out of
a total 36 reviews published in RMP so far, authored/coauthored by
at least one scientist from India, since 1929; source:
'Affiliation' India search at the journal site  Errata excluded)], 10
books [3 Cambridge Univ. Press, 2 Oxford Univ. Press, 3 Springer, 2 WileyVCH]. For citations etc., see
Google Scholar and
ResearchGate.
A few representative
♦ (Review) Papers :
 Dynamic Transitions and Hysteresis
(with M. Acharyya), Reviews of Modern Physics (1999)
 Kinetic Exchange Models for
Income and Wealth Distributions (with A. Chatterjee), European Physical
Journal (2007)
 Quantum Annealing and Analog Quantum
Computations (with A. Das), Reviews Modern Physics Physics (2008)
 Failure Processes in Elastic Fiber Bundles
(with A. Hansen & S. Pradhan), Reviews of Modern Physics(2010)
 Statistical Physics of Fracture, Friction and
Earthquakes
(with S. Biswas, T. Hatano, N. Kato & H. Kawamura), Reviews of Modern Physics
(2012)
 Statistical
Mechanics of Competitive Resource
Allocation using AgentBased Models (with A. Chakraborti,A. Chatterjee,
D. Challet, M. Marsili & Y.C. Zhang), Physics Reports (2015).
&
♦ Books :

Econophysics of Income & Wealth Distributions (with A. Chakraborti, S. R. Chakravarty & A. Chatterjee), Cambridge Univ. Press, Cambridge (2013)
 Sociophysics: An Introduction (with P. Sen), Oxford Univ. Press, Oxford (2014)
 Quantum Phase Transitions in Transverse Field Spin Models:
From Statistical Physics to Quantum Information (with G. Aeppli,
U. Divakaran, A. Dutta, T. F. Rosenbaum & D. Sen),
Cambridge Univ. Press, Cambridge & Delhi

Statistical Physics of Fracture, Breakdown & Earthquake
(with S. Biswas & P. Ray), WileyVCH, Berlin (2015).
 Quantum Spin Glasses, Annealing and Computation
(with S. Tanaka & R. Tamura), Cambridge Univ. Press, Cambridge & Delhi (2017) [Contract signed between MorikitaShuppan & CUP for Japanese Edition, 2017]
 Econophysics of the Kolkata Restaurant Problem and Related Games:
Classical and Quantum Strategies for Multiagent, Multichoice Repetitive Games (with A. Chatterjee, A. Ghosh, S. Mukherjee & B. Tamir), New
Economic Windows Series, Springer International Publishing, Switzerland
(2017),
( See also).
Supervised Ph.D. theses of:
S. S. Manna (1987)
* A. K. Roy (1988)
* P. Ray (1989)
* M. Ghosh (1992)
* P. Raychaudhuri (Sen) (1993)
* K. Barat (1995)
* M. Acharyya (1996)
* A. Dutta (2000)
* P. Bhattacharyya (2000)
* A. Misra (2001)
* A. Chakraborti (2003)
* S. Pradhan (2005)
* A. Chatterjee (2008)
* A. Das (2008)
* A. Ghosh (2014)
* S. Biswas (2015) * A. Rajak (Jointly with A. Basu; 2016) .
Journal Editorial Board member of: ♦ European Physical Journal
B (present) ♦
Indian Journal of Physics (present) ♦ Journal of Economic
Interaction and Coordination (present) ♦ Journal of Magnetism & Magnetic Materials (past)
♦ Natural Science (past)
♦ Pramana  Journal of Physics (past) ♦ Scientific Reports (present) ♦ SciPost (present)
Book Series Editor of: ♦
Physics of Society: Econophysics
& Sociophysics (with M. Gallegati, A. Kirman & H. E. Stanley)
of Cambridge University Press
♦ Statistical Physics of Fracture & Breakdown (with Purusattam Ray), Wiley:
I, II, III, IV ♦ New Economic Windows series, Springer
AWARDS & DISTINCTIONS:
 Young Scientist Award of INSA (1984)
 Professeur Invité, University of Paris, UP13, LabPMTM, CNRS (1988)
 Shanti Swarup Bhatnagar Award, CSIR India (1997)
 Fellow, Indian Academy of Sciences, Bangalore (Elected, 1997)
 Fellow, Indian National Science Academy, New Delhi (Elected, 2003)
 Honorary Visiting Professor, Indian Statistical Institute, Kolkata (2007 )
 Outstanding Referee Award of the American Physical Society (2010)
 Professeur Invité, École Centrale Paris (2010)
 J C Bose National Fellow, DST India (2011'20)
 Executive Editor (Region: India)
European Physical Journal B (2016 )
 Honorary Emeritus Professor, S. N. Bose National Centre for Basic Sciences, Kolkata (2018 )
 Father of Econophysics, Thesis, Dept. History and Philosophy of Science, University of Cambridge (2018)
CONTACT:
*************************************
CITATIONS OF OUR WORK INCLUDE:
♦
Editorial of Topical Issue on Physics in
Society,
The European Physical Journal B, Vol 57 (2007) pp 121125, incorporating
2 of ours, in an Editorial Choicelist of 21 "exemplifying pioneering"
publications
(earliest in 1872)
in "Economy & Political
Economy".
♦ Discussions on "pioneering"
papers from
"Chakrabarti's research group" (p 187; pp 185206) in Applied
Partial Differential Equations (by P A Markowich) Springer, Berlin
(2007).
♦
Entry on Econophysics (by J. Barkley Rosser, Economist)
in The New Palgrave Dictionary of Economics, 2nd Ed., Vol 2,
Macmillan, NY (2008), pp 729732, beginning with "According to Bikas
Chakrabarti (...), the term 'econophysics' was neologized in 1995
at the second StatphysKolkata conference in Kolkata (formerly Calcutta),
India ..." . * Also, Econophysics has been assigned
the Physics and Astronomy Classification Scheme (PACS)
number 89.65Gh by the American Institute of Physics.
♦
Discussions on "influential" papers (p. 2803)
from "Kolkata School" (p. 2808; pp. 28002826; see also pp. 27922800)
in Encyclopedia of Complexity &
System Science, Vol. 3, Springer, New York
(2009); *
Discussions on "influential" (p. 1705) & "elegant" (p. 1711)
papers
from "Kolkata School" (p. 1711) by V M Yakovenko (Physics) & J Barkley Rosser (Economics) in Reviews of Modern Physics (2009).
♦
Feature article on "The Physics of our Finances", saying "So in
2000, Bikas Chakrabarti's team in the Saha Institute of Nuclear Physics
in Kolkata, India ... [introduced another model with distributed savings,
and with] this tweak, the model correctly reproduced the whole
wealth distribution curve ... If these simple models do capture something
of the essence of the realworld economics, then they offer some
good news." , p. 41, New Scientist, 28 July, 2012
[See reproduced in the last section of this document].
♦ Special issue on "Econophysics: Perspectives & Prospect",
saying "The physicists, however, did not present a parallel
perspective of this social science, at least not until recently
when eminent physicists like Eugene H. Stanley, Bikas K. Chakrabarti,
J. Doyne Farmer, JeanPhilippe Bouchaud and many others having
joined the fray to create this new field which has now started to
gain academic respect. ... As mentioned, Kolkata, India, occupies a
crucial role in the history of this new science which has amongst
its pioneers an Indian face, too. Bikas Chakrabarti of Saha
Institute of Nuclear Physics, an eminent condensed matter physicist
in his own rights, is, along with Stanley, one of the foremost
contributors to this field. ...", in the
Editorial
and "... He (Bikas) likes to make something really happen. So he
started to have meetings on econophysics and I think the
first one was probably in 1995 (he decided to start it in 1993–1994).
Probably the first meeting in my life on this field that I went to
was this meeting. In that sense Kolkata is — you can say — the nest
from which the chicken was born and Bikas gets, deservingly so, a lot
of credit for that because it takes a lot of work to have a meeting
on a field that does not really exist, so to say! After all who is
going to come? If you have a meeting on standard fields like
superconductivity there are many people who were happy to come to
India to attend that meeting, but econophysics was something
different. So he should get a lot of credit for this. ..." ,
said Eugene Stanley in his Interview (pp. 7378) in
IIM Kozhikode
Society & Management Review, Vol. 2 (July 2013)
© 2013 Indian Institute of Management Kozhikode, SAGE Publications. ♦ The book Interacting Multiagent Systems, Oxford Univ. Press (2014) by Pareschi & Toscani (Dept.
Math., Univs. Ferrara & Pavia) dicussed the "ChakrabortiChakrabarti model"
as well as "ChatterjeeChakrabartimanna model" of income/wealth
distributions in sections 5.3 (p. 167),
5.7 (pp. 205210) and elsewhere. * In their paper Physica A (2016), Pareschi, Velluccci &
Zanella (Dept. Math., Comp. Sc. & Engg., Univs. Ferrara & Rome) say "After
the seminal models for wealth/opinion exchange
for a multiagent system
introduced in Chakraborti & Chakrabarti (European Physical Journal B, 2000), Toscani (Communications in Mathematical
Sciences, 2006) and Sen & Chakrabarti (Sociophysics: An Introduction, Oxford
Univ. Press, 2013) some recent works considered ...". * The book
Guidance of an Enterprise Economy, MIT Press (2016)
by Shubik & Smith (Math. Inst. Economics, Yale
University & Santa Fe Institute) noted: "It was shown in Chakraborti
& Chakrabarti (European Physical Journal B, 2000) that uniform saving
propensity of the agents constrains the entropy maximizing dynamics in
such a way that the distribution becomes gammalike, while (quenched)
nonuniform saving propensity of the agents leads to a steady state
distribution with a Paretolike powerlaw tail (Chatterjee, Chakrabarti
& Manna, Physica A, 2004). A detailed discussions of such steady state
distributions for these and related kinetic exchange models is provided
in Econophysics of Income & Walth Distributions (Chakrabarti, Chakraborti,
Chakravarty & Chatterjee, Cambridge University Press, 2013)." in pp. 7576
and elsewhere.
♦ The book
MacroEconophysics,
Cambridge University Press (2017), by
Aoyama, Fujiwara, Ikeda, Iyetomi, Souma & Yoshikawa (Depts.
Physics & Economics, Univs. Kyoto, Hyogo,
Niigata, Nihon & Tokyo), begins with a "Foreword" from Bikas K. Chakrabarti.
# In the section on "The position of econophysics in the disciplinary space" in
Econophysics and Financial
Economics, Oxford Univ. Press (2017), by Jovanovic & Schinckus,
Department of Finance, University of Leicester, the authors
write (pp. 83, 178) :
"To analyze the position of
econophysics in the disciplinary space, the most influential
authors in econophysics were identified. Then their papers in
the literature were tracked by using the Web of Science database
of ThomsonReuters ... The sample is composed of Eugene Stanley,
Rosario Mantegna, Joseph McCauley, Jean Philippe Bouchaud, Mauro
Gallegati, Benoit Mandelbrot, Didier Sornette, Thomas Lux, Bikas
Chakrabarti, and Doyne Farmer." ♦ In the thesis
When
Physics Became Undisciplined: An Essay on Econophysics
(August 2018, Department of History and Philosophy
of Science, University of Cambridge), Schinckus writes (pp. 1516) "In
order to reconstruct the subfield of econophysics,
I started with the group of the most influential
authors in econophysics and tracked their papers in
the literature using the Web of Science database of Thomson
Reuters (The sample is composed of: Eugene Stanley, Rosario
Mantegna, Joseph McCauley, JeanPierre Bouchaud,
Mauro Gallegati, Benoît Mandelbrot, Didier Sornette, Thomas
Lux, Bikas Chakrabarti and Doyne Farmer). These key authors
are often presented as the fathers of econophysics
simply because they contributed significantly to its early
definition and development. Because of their influential
and seminal works, these scholars are actually the
most quoted authors in econophysics. Having the 10
highest quoted fathers of econophysics as a sample
sounds an acceptable approach to define bibliometrically
the core of econophysics."
♦ In their review paper on Wealth & Income Distribution
International Journal of Social Science and Economic Research (January, 2019),
de Paz et al., (Faculty of Engg., National Autonomous University
of Mexico) write "There were three outstanding pioneering
works in adopting the ideal gas model in which each agent
represents a gas molecule trading money in an elastic
collision: Bouchaud & Mézard [Physica A (2000)], Chakraborti &
Chakrabarti )] [European Physical Journal B (2000)] and Drăgolescu &
Yakovenko [European Physical Journal B (2000)].".
♦
FOCUS article "Breakthrough in Quantum Computation", saying
"A new class of
quantum computers utilizing quantum tunneling has been achieved
(as pioneered by DWave with their 128 superconducting logic elements).
The idea of computation using quantum annealing technique was first mooted
by a group of Calcutta based scientists ..." in its Editorial Note, and saying "... The seminal proposal (of Bikas Chakrabarti and his team from Saha Institute of Nuclear Physics, Calcutta) was taken up by other groups in the world ...", in a Comment by Indrani Bose, appeared in
Science & Culture (Indian Science News Association),
Vol. 79 (Sept.Oct, 2013)
pp. 381382.

For continuing discussions, see Nature Physics (March 2014) by Boixo et al. (Univ. S. California,
ETH, ...) saying "The phenomenon of quantum tunneling suggests that it
can be more efficient to explore the state space quantum mechanically in a
quantum annealer [Ray, Chakrabarti & Chakrabarti Physical Review B (1989);
Finnila et al., Chemical Physics Letters (1994); Kadowaki & Nishimori,
Physical Review E (1998)]." ; * International Journal of Quantum
Information (June 2014) by Cohen & Tamir (Tel Aviv & BarIlan
Univs.) saying "Quantum annealing was first discussed by Ray
et al. in 1989 [Ray, Chakrabarti & Chakrabarti, Physical Review (1989)]."; * and the collection of 'Discussion & Debate' papers
on Quantum Annealing: The Fastest Route to Quantum Computation? European Physical
Journal: Special Topics (January 2015), where e.g.,
Silevitch, Rosenbaum & Aeppli (Univ. Chicago, Caltech, Swiss Fed. Inst.
Tech., ...) say "A quantum computer has the potential to
exploit effects such as entanglement and tunneling and that appear on the
atomic and molecular size scales to solve such problems dramatically
faster than conventional computers [Ray, Chakrabarti & Chakrabarti,
Physical review B (1989); Farhi et al., Science (2001); Santoro et al,
Science (2002), Das & Chakrabarti, Reviews of Modern Physics (2008);
Johnson et al., Nature (2011)].".
 Heim et al.
(ETH & Google, Zurich) in
Science (April 2015)
say "Quantum annealing
[Ray, Chakrabarti & Chakrabarti, Physical
Review B (1989); Finnila et al., Chemical Physics Letters
(1994); Kadowaki & Nishimori, Physical Review E (1998);
Farhi et al., Science (2001); Das & Chakrabarti, Reviews
of Modern Physics (2008)] uses quantum tunneling
instead of thermal
excitations to escape from local minima, which can be advantageous in systems
with tall but narrow barriers, which are easier to tunnel through than to
thermally climb over.".
Mandra, Guerreschi, and AspuruGuzik (Dept. Chem., Harvard Univ. ) in their
Physical Review A (December 2015) begin
with the introductory sentence "In 2001, Farhi et al. [Science
(2001)] proposed a new paradigm to carry
out quantum computation ... that builds on previous results developed by the
statistical & chemical physics communities in the context of quantum
annealing techniques [Ray, Chakrabarti & Chakrabarti, Physical Review B
(1989); Kadowaki & Nishimori, Physical Review E (1998);
Finnila et al., Chemical Physics Letters (1994); Lee & Berne, Journal of
Physical Chemistry A (2000)].".
 Boixo et al. (Google & NASA Ames, California; Michigan State Univ., Michigan; DWave Systems & Simon Fraser Univ., British Columbia; & acknowledging
discussions with Farhi, Leggett, et al.)
in their Nature Communications (January 2016) start
the paper with the sentence "Quantum annealing
[Finnila et al. Chemical Physics Letters (1994); Kadowaki &
Nishimori, Physical Review E (1998); Farhi et al., arXiv (2002);
Brooke et al., Science (1999);
Santoro et al., Science (2002)]
is a technique inspired by classical simulated annealing [Ray,
Chakrabarti & Chakrabarti, Physical Review B (1989)] that
aims to take advantage of quantum tunnelling.".
 Tran et al. (Quantum AI Lab & Intelligent Systems Division, NASA Ames, ...)
in their Technical Report no. WS1612, Proc. 30th AAAI Conf. on AI (March 2016) on 'Scheduling a Mars Lander ' say "While
largescale universal quantum computers are likely decades away, special
purpose quantum computational devices are emerging. The
first of such are quantum annealers, special purpose hardware designed
to run quantum annealing [Farhi et al.,
arXiv (2000); Das & Chakrabarti, Reviews of Modern Physics
(2008); Johnson et al. Nature (2011); Smelyanskiy et al.,
arXiv (2012)], a metaheuristic that can make use of certain
nonclassical effects, such as quantum tunneling and quantum interference
[Das & Chakrabarti, Reviews of Modern Physics (2008); Boixo
et al., arXiv (2014)]
for computational purposes.".
 Wang, Chen & Jonckheere (Dept. Electr. Engg., Univ. S. California) begin their
Scientific
Reports (May, 2016)
by saying "Quantum annealing ...
is a generic way to efficiently get closetooptimum solutions in many NPhard
optimization problems ... (&) is believed to utilize quantum tunneling
instead of thermal hopping to more efficiently search for the optimum solution
in the Hilbert space of a quantum annealing device such as the DWave
[Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Kadowaki &
Nishimori, Physical Review E (1998)].".

Matsuura et al. (Niels Bohr Inst.; Yukawa Inst.; Tokyo Inst. Tech.; Univ.
S. California) in their Physical Review Letters (June, 2016)
introduce by saying "Quantum annealing, a quantum
algorithm to solve optimization problems [Kadowaki & Nishimori, Physical
Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);
Brooke et al., Science (1999); Brooke et al., Nature (2001); Santoro et al.,
Science (2002); Kaminsky et al., Quantum Computing (Springer, 2004)]
that is a special case of universal adiabatic quantum computing, has
garnered a great deal of recent attention as it provides an accessible path
to largescale, albeit nonuniversal, quantum computation using presentday
technology.". La Cour, Troupe & Mark (Appl. Res. Lab., Univ. Texas at Austin) write
in the Introduction of their
Journal of Statistical Physics (June, 2016) , "A related
optimization procedure, quantum annealing, has been proposed for solving hard
optimisation problems [Farhi et al, Science (2001); Das & Chakrabarti, Reviews
of Modern Physics (2008)]. ... Several generations of devices that implement
quantum annealing for the Ising model have been built by Dwave systems, Inc.
and used to solve a variety of optimisation problems ... ."
 Yao et al. (Depts. Physics, Univ. California, Berkeley, Harvard Univ.,
Cambridge, Stanford Univ., California) in their arXiv (July, 2016) ,
discussed, both theoretically and experimentally, the fast scrambling
or thermal and localized regions of the transverse Ising SK models, following
[Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)] and compared
their results (see their Fig. 2 caption) with those reported in [Mukherjee,
Rajak & Chakrabarti, Physical Review E (2015)]
Muthukrishnan, Albash & Lidar (Depts. Physics, Chemistry, Electrical
Engineering, ..., Univ. S. California) write
in the Introduction of their
Physical Review X (July, 2016) , "It is often stated that
quantum annealing [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);
Finnila et al. Chemical Physics Letters (1994); Kadowaki &
Nishimori, Physical Review E (1998); Farhi et al., Science (2001); Das &
Chakrabarti, Reviews of Modern Physics (2008)] uses tunneling instead
of thermal excitations to escape from local minima, which can be advantageous
in systems with tall but thin barriers that are easier to tunnel through
than to thermally climb over [Heim et al., Science (2015); Das &
Chakrabarti, Reviews of Modern Physics (2008), Suzuki, Inoue & Chakrabarti,
Quantum Ising Phases & Transitions, Springer (2013)]. ... We demonstrate that
the role of tunneling is significantly more subtle ...". Knysh (NASA Ames, California) in his investigations in
Nature Communications (August, 2016) on
some eventual "bottlenecks", starts by
writing "Quantum algorithms offer hope for tackling computer
science problems that are intractable for classical
computers. ... Those problems are targeted by the quantum
adiabatic annealing algorithm [Kadowaki & Nishimori, Physical Review
E (1998); Farhi et al., arXiv (2000); Das & Chakrabarti, Reviews
of Modern Physics (2008)]."  Cao et al. (Purdue Univ., Indiana, Marquette Univ., Wisconsin) write
in the first two lines of their paper in
Scientific Reports (September, 2016) "Quantum annealing (QA) uses
the principles of quantum mechanics for solving unconstrained optimization
problems [Finnila et al. Chemical Physics Letters (1994)], Kadowaki &
Nishimori, Physical Review E (1998), Farhi et al., Science (2001),
Das & Chakrabarti, Quantum Annealing & Related Optimization Methods, Springer
(2005)]. Since the initial proposal of QA, there has been much interest
in the search for practical problems
where it can be advantageous with respect to classical algorithms
[Das & Chakrabarti, Quantum Annealing & Related Optimization Methods,
Springer (2005), Das & Chakrabarti, Reviews of Modern Physics (2008), ...],
particularly simulated annealing ... .".
Takata et al (Japan
Sc. & Tech. Agency; Univ. Tokyo; Stanford Univ.) in their
Scientific Reports (September, 2016) write "Metaheuristic
algorithms have been vastly studied to attack this (NP hard)
intractable problem. Simulated annealing (SA) is one of the most
prevalent and successful methods in practice. Quantum annealing
(QA) [Kadowaki & Nishimori, Physical Review E (1998); Das & Chakrabarti,
Reviews of Modern Physics (2008)] has been proposed as a
method which can potentially give better solutions than SA.
The hardware to implement QA has also been recently developed
and its true performance is under consideration.".
 Wild et al. (Depts. Phys. & Engg., Harvard Univ.; Caltech; CUNY; Tech. Univ. Munich; Univ. California Berkeley) in their Physical Review Letters (October 2016)
start by saying "The adiabatic theorem provides a powerful tool to
characterize the evolution of a quantum system under a timedependent
Hamiltonian. ... Adiabatic evolution can also serve as a platform for
quantum information processing [Farhi et al., arXiv 2000; Farhi et al.,
Science (2001); Das & Chakrabarti, Reviews of Modern Physics (2008);
Bapst et al., Physics Reports (2013), Santoro & Tosatti, Journal of
Physics A: Math. Gen. (2006); Laumann et al., European Physical
Journal: Spl. Top. (2015)].".
 Chancellor et al. (Depts. Phys. & Engg., Univs. Durham, Oxford, London)
in the introduction of their
Scientific Reports (November, 2016) say "There have been many
promising advances in quantum annealing, since the idea
that quantum fluctuations could help explore rough energy landscapes
[Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)], through
the algorithm first being explicitly proposed [Finnila et al. Chemical
Physics Letters (1994)], further refined [Kadowaki &
Nishimori, Physical Review E (1998)], and the basic concepts
demonstrated experimentally in a condensed
matter system [Brooke et al., Science (1999)]. ... For an overview ... see Das & Chakrabarti, Reviews of Modern Physics (2008).".
 Rams, Mohseni & del Campo (Instute of Physics, Krakow; Google Quantum
AI, Venice, CA & Univ. Massachusetts, Boston) start their
New Journal of Physics (December, 2016) paper with the sentence
"Techniques to control or assist adiabatic dynamics are of broad interest
in quantum technologies, including quantum simulation and quantum computation
[Das & Chakrabarti, Reviews of Modern Physics (2008), Cirac & Zoller,
Nature Physics (2012)].".
 Ohzeki (Tohoku University) start his Scientific Reports (January, 2017)
paper with "Quantum annealing (QA)... was originally proposed as a numerical
computational algorithm [Kadowaki & Nishimori, Physical Review E (1998)]
inspired by simulated annealing [Kirkpatrick, Gelatt & Vecchi,
Science (1983)]
, and the exchange Monte Carlo simulation [Hukushima & Nemeto Journal
of the Physical Society of Japan (1996)]. In QA, the quantum tunneling
effect efficiently finds the ground state even in the manyvalley structure
of the energy landscape therein [Ray, Chakrabarti & Chakrabarti, Physical
Review B (1989), Apolloni, Carvalho & de Falco, Stochastic Process & their
Applications (1989), Das & Chakrabarti, Reviews of Modern Physics (2008)].".
 Dridi & Alghassi (1QB Information Technologies, Vancouber) in their
Scientific Reports (February, 2017) mentions in their introduction
"Prime factorization also
connects to many branches of mathematics; two branches relevant to us
are computational algebraic geometry [Cox et al., Using Algebrig Geometry,
Springer, 1998] and quantum annealing [Kadowaki & Nishimori, Physical
Review E (1998); Farhi et al., Science (2001); Das & Chakrabarti, Reviews
of Modern Physics (2008)].".

Smelyanskiy et al. (Google & NASA Ames, California; Michigan
State Univ., Michigan; etc.) start their paper Physical Review Letters (February, 2017) with
"Quantum annealing (QA) has been proposed as a candidate for a speedup
of solving hard optimization problems
[Kadowaki & Nishimori, Physical Review E (1998); Brooke et al.,
Science (1999); Farhi et al., Science (2001)]. ...
Conventionally, QA is related to quantum tunneling in the landscape
that is slowly varied in time
[Das & Chakrabarti, in Quantum Annealing & Related Optimization
Methods, Eds. Das & Chakrabarti, Springer (2005)].".
 Mandrà, Zhu & Katzgraber (Harvard Univ., Massachusetts; NASA Ames, California;
Texas A & M Univ, Texas; Santa Fe Institute, New Mexico; etc.) in their
Physical Review Letters (February, 2017) mentions in their
introduction
"More
recently, the quantum counterpart of simulated annealing
(usually called “quantum annealing”) was suggested [Finnila et al.,
Chemical Physics Letters (1994); Kadowaki & Nishimori, Physical Review E (1998);
Brooke et al., Science (1999); Farhi et al., Science (2001); Santoro et al.,
Science (2002), Das & Chakrabarti, in Quantum Annealing & Related Optimization
Methods, Eds. Das & Chakrabari, Springer (2005); Santoro & Tosatti, Journal of Physics A (2006); Das
& Chakrabarti, Reviews of Modern Physics (2008); Morita & Nishimori, Journal
of Mathematical Physics (2008)].".
 Azinovic et al. (ETH Zurich; RIKEN, Wakoshi; Microsoft
Research, Redmond; etc.) in their
SciPost
Phys (April, 2017) says
"While Simulated Annealing makes use of thermal excitations
to escape local minima, quantum annealing [Ray,
Chakrabarti & Chakrabarti, Physical Review B (1989);
Finniela et al., Chemical Physics Letters (1994), Kadowaki & Nishimori,
Physical Review E (1998); Farhi et al., Science (2001); Das & Chakrabarti,
Reviews of Modern Physics (2008)] uses quantum fluctuations to find
the ground state of a system .".
 Zhang et al. (Stanford Univ., California; Cray, Seattle; Universidad
Complutense, Madrid; Univ. Southern California, Los Angeles) in their
Scientific Reports (April, 2017) says in the introduction "Quantum
annealers [Kadowaki & Nishimori, Physical Review E (1998);
Farhi et al., Science (2001)] provide a unique approach to finding
the groundstates of discrete optimization problems, utilizing gradually
decreasing quantum fluctuations to traverse barriers in the energy
landscape in search of global optima, a mechanism commonly believed to
have no classical counterpart [Kadowaki & Nishimori, Physical
Review E (1998); Farhi et al., Science (2001); Finnila et al., Chemical
Physics Letters (1994); Brooke et al., Science (1999); Santoro et al.,
Science (2002); Das & Chakrabarti, Reviews of Modern Physics (2008);
Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)].".
 Hormozi et al. (MIT, Massachusetts; ETH Zurich, Zurich; Microsoft Research,
Washington; etc.) in the Introduction of their paper
Physical Review B (May, 2017) says "A quantum annealing device is a machine that physically implements this approach by realizing a
timedependent Hamiltonian, which attempts to follow the adiabatic quantum
algorithm [Farhi et al., arXiv:quantph/0001106 (2000);
Farhi et al., Science (2001)]; Das & Chakrabarti, Reviews of Modern
Physics (2008)]."
 Mott et al. (Depts. Physics & Electrical Engg., Caltech, California; Univ.
Southern California, California) write in the 3rd line of their letter
Nature (October, 2017) write "Here we use quantum
[Kadwaki & Nishimori, Physical Review E (1998); Das & Chakrabarti,
Reviews of Modern Physics (2008), Neven et al., arXiv/0811.0416 (2008);
Pudenz & Lidar, Quantum Information Processing (2013)] and classical
[Kirkpatrick
et al., Science (1983); Katzgraber et al., Journal of Statistical Mechanics
(2006)] annealing (probabilistic techniques for approximating the global
maximum or minimum of a given function) to solve a Higgs
signalversusbackground machine learning optimization problem,
mapped to a problem of finding the ground state of a corresponding
Ising spin model."
 Bottarelli et al. (Univ. Verona, Verona), in their FOCUS paper in
Soft Computing
(January, 2018) mentions, while discussing in the section on Quantum
Annealing (QA) & DWave quantum annealers/computers,
"The advantage of QA is the dependency of the
tunneling probability both on
the height and the width of the potential barrier, which gives
it the ability to move in an energy landscape where local
minima are separated by tall barriers, provided that they are
narrow enough [Ray, Chakrabarti & Chakrabarti, Physical Review B
(1989)].".

Albash & Lidar (Univ. Southern California) in their review paper
Reviews of Modern Physics (January, 2018) note that the exponential run time problem in classical
annealing comes from "... energy barriers in the
classical cost that scale with problem size to foil singlespin
update Simulated Annealing (SA). This agrees with the intuition
that a Stoquastic Adiaabatic Quantum Comuptation
advantage over SA is associated with tall and thin barriers
[Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Das & Chakrabarti,
Reviews of Modern Physics (2008)].". Additional discussions on these and
Das, Chakrabarti & Stinchcombe, Physical Review E (2005); Rajak & Chakrabarti,
Indian Journal of Physics (2014) & Suzuki, Inoue, Chakrabarti, Quantum Ising
Phases & Transitions in Transverse Ising Models, Springer (2013) are
also included.
 Baldassi & Zechchina (Bocconi Inst., Milan & ICTP, Trieste)
start their paper
Proceedings of the National Academy of Science (February, 2018) with the sentence "Quantum annealing aims at finding
lowenergy configurations of nonconvex optimization problems by a
controlled quantum adiabatic evolution, where a timedependent
manybody quantum system which encodes for the optimization problem
evolves toward its ground states so as to escape local minima through
multiple tunneling events
[Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);
Finnila et al., Chemical Physics Letters (1994); Kadwaki & Nishimori,
Physical Review E (1998); Farhi et al., Science (2001); Das & Chakrabarti,
Reviews of Modern Physics (2008)].".
 RodrıguezLaguna and Santalla (Univ. Madrid) in their paper on "Building
an Adiabatic Quantum Computer Simulation in the Classroom"
American Journal of Physics (May, 2018) start their Introduction by saying "Interest in
quantum computation is increasing lately, since it might be the next
quantum technology to take off. Exciting new spaces for exploration have
appeared, ... [and among them] we have chosen adiabatic quantum computation
[Farhi et al., Science (2001); Das & Chakrabarti, Reviews of Modern
Physics (2008); Santoro et al., Science (2002)] and developed a gentle
introduction which can be delivered in two sessions, a theoretical and a
practical one. ... [See also] [Suzuki, Inoue & Chakrabarti, Quantum
Ising Phases & Transitions, Springer (2013)].". Also, Moran (Caltech)
in her "Quintuple: A Tool for Introducing Quantum Computing into the Classroom" Frontiers in Physics (July, 2018) writes "This paper focuses on
universal gate quantum computation, but it is useful to note the
plethora of work in quantum computing focusing on quantum annealing [Das
& Chakrabarti, Reviews of Modern Physics (2008); Albash &
Lidar, Reviews of Modern Physics (2018); Tanaka, Tamura &
Chakrabarti, Quantum Spin Glasses, Annealing & Computation,
Cambridge Univ. Press (2017).".
 Mishra, Albash & Lidar (Depts. Physics, Chemistry, Electrical Engineering,
Univ. Southern California)
begin their paper
Nature Communications (July, 2018) with the sentence "Quantum
annealing
[Apolloni, Carvalho & de Falco, Sotcastic Processes & Applications (1989);
Apolloni, CesaBianchi & de Falco, in Stochastic Process, Physics & Geometry,
World Scientific (1990); Ray, Chakrabarti & Chakrabarti, Physical
Review B (1989); Somoraji, Journal of Physical Chemistry (1991);
Amara, Hsu & Straub (1993), Journal of Physical Chemistry (1993);
Finnila et al., Chemical Physics Letters (1994); Kadwaki & Nishimori,
Physical Review E (1998); Das & Chakrabarti,
Reviews of Modern Physics (2008)], also known as the quantum adiabatic
algorithm [Farhi et al. arXiv (2000); Farhi et al., Science (2001)]
or adiabatic quantum optimization [Smelyanski, Toussaint &
Timukin, arXiv (2001); Reichardt, in Proceedings of the ACM Symposium
on Theory of Computing: ACM36 (2004)] is a
heuristic quantum algorithm for solving combinatorial optimization
problems.".
 Venuti & Lidar (Depts. Physics, Chemistry, Electrical Engineering,
Univ. Southern California)
begin their paper
Physical Review A (August, 2018), saying "Quantum annealing
and adiabatic quantum computation are promising candidates in the search
for quantumenhanced information processing [Das & Chakrabarti,
Reviews of Modern Physics (2008), Albash & Lidar, Reviews of Modern Physics
(2018)]. Both can be viewed as adiabatic state preparation protocols
[Aharonov & TaShma, in Proc. 35th Annual ACM Symposium on
Theory of Computing (2013)], where the target state is typically the
solution to a computational problem such as optimization, or a state
from a distribution that one wishes to sample from.".
 Pichler et al. (HarvardSmithsonian Center, Dept. Physics, Harvard Univ., Cambridge & Univ. California, Berkeley) begin their arXiv (August 2018) paper with the (first two) sentences "Quantum optimization is a paradigm to solve combinatorial optimization problems by utilizing controlled dynamics of quantum manybody systems [Farhi et al., Science (2001); Kadwaki & Nishimori,
Physical Review E (1998); Das & Chakrabarti,
Reviews of Modern Physics (2008); Albash & Lidar,
Reviews of Modern Physics (2018)]. The key idea is to steer the dynamics of quantum systems such that their final states provide solutions to optimization problems [Das & Chakrabarti,
Reviews of Modern Physics (2008)].". See also, * arXiv
(September, 2018)
by Schuetz et al. (Harvard Univ.,
Innsbruck Univ, Kavli Inst. & Max Planck Inst.), providing "... a natural
architecture for the implementation of quantum algorithms, such as quantum
annealing [Das & Chakrabarti, Reviews of Modern Physics (2008)] or ..."
as mentioned in its Introduction, and * Pichler et al.
(HarvardSmithsonian Center, Dept. Physics, Harvard Univ.,
Cambridge & Univ. California, Berkeley) beginning their arXiv
(September, 2018) paper with the sentence "Various quantum
algorithms have been proposed in recent years to solve combinatorially
hard optimization problems [Farhi et al., Science (2001); Smelyanski,
Toussaint & Timucin, arXiv (2001); Das & Chakrabarti, Reviews of Modern Physics
(2008); Albash & Lidar, Reviews of Modern Physics (2018); Santoro et al.,
Science (2002); Boixo et al., Nature Communication (2013); Johnson et al.,
Nature (2011); Ronnow et al., Science (2014); Houck, Tureci & Koch, Nature
Physics (2012); Smolin & Smith, arXiv (2013); Wang et al., arXiv (2013); Shin
et al., arXiv (2014); Harrow & Montanaro, Nature (2017)].
 Jiang et al. (Dept. Computer Science, Purdue Univ., Quantum Computing
Institute, Oak Ridge National Laboratory) reporting on their quantum
annealing framework for prime number factorization in
Scientific Reports (December, 2018) write "In this contribution, we
introduce a new procedure for solving the integer factorization problem
using quantum annealing [Kadwaki & Nishimori, Physical Review E (1998);
Das & Chakrabarti, Reviews of Modern Physics (2008)] which utilizes
adiabatic quantum computation. ... Quantum
Annealing was introduced [Kadwaki & Nishimori, Physical Review E (1998)]
to solve optimization problems using quantum fluctuations to transit to
the ground state, compared to simulated annealing which uses thermal
fluctuations to get to the global minimum. Quantum fluctuations such as
quantum tunneling [Ray, Chakrabarti & Chakrabarti, Physical
Review B (1989)] provide ways of transitions between states. The
transverse field controls the rate of the transition, as the role of
temperature played in simulated annealing.".

Vepsäläinen, Danilin & Paraoanu (Dept. Appl. Physics, Aalto Univ.),
reporting on adiabatic manipulation of the quantum state
in quantum information processing in
Science (February, 2019) write in the Introduction
"For adiabatic quantum computing
[Farhi et al., Science (2001)], quantum annealing [Das &
Chakrabarti, Reviews of Modern Physics (2008), Johnson et al., Nature (2011)] ,
and holonomic quantum computing [Sjöqvist et al., New Journal of Physics
(2012); Zanardi & Rasetti, Physics Letters A (1999); Abdumalikov et al.,
Nature (2013)], shortcuts to adiabaticity would be one important route
to quantum advantage [Boixo et al., Nature Physics (2014)].".  Dridi, Alghassi & Tayur (Quantum Computing Group, Carnegie Mellon Univ.)
in their review paper on computational algebraic geometry and quantum
optimization
(arXiv, March 2019; Comments: Commemorating 30 years since
the publication of Ray, Chakrabarti & Chakrabarti, Phys. Rev. B 39 (1989)
11828; Journal reference: Special issue of Science & Culture, 2019 )
write in their Summary & Discussion section "As we mentioned in the
Introduction, we are travelers in a journey that our ancients started.
Evidence of 'practical mathematics' during 2200 BCE in the Indus Valley
has been unearthed that indicates proficiency in geometry. Similarly,
in Egypt (around 2000 BCE) and Babylon (1900 BCE) ... Algebra ...
reached a new high watermark during the golden age of Islamic mathematics
around 10th Century AD ... The next significant leap in algebraic
geometry, a 'Renaissance', in the 16th and 17th century, is
quintessentially European ... Computational algebraic geometry begins
with the Buchberger in 1965 ... Magnetism simply could not be
explained by classical physics, and had to wait for quantum mechanics.
The workhorse to study it mathematically is the Ising model, conceived
in 1925. Quantum computing was first introduced by Feynman in 1981
[Feynman, International Journal of Theoretical Physics (1982)]. The
study of Ising models that formed a basis of physical realization of
a quantum annealer (like DWave devices) can be traced to the
1989 paper by Ray, Chakrabarti and Chakrabarti
[Physical Review B (1989)]. Building on various adiabatic theorems
of the early quantum mechanics and complexity theory, adiabatic quantum
computing was proposed by Farhi et al. in 2001 [Science (2001)].
Which brings us to current times. The use of computational algebraic
geometry ... in the study of adiabatic quantum computing ..., is
conceived by us, the authors, of this expository article. Let us
close with the Roman poet Ovid (43 BC17 AD): 'Let others praise
ancient times; I am glad I was born in these.'.".
 Sato et al. (School of Sc. & Engg., Saitama Univ.; Fujitsu Laroratories;
Japan Science & Technology)
write in the Introduction of their paper
Physical Review E (April, 2019) "There are two famous
annealing concepts [Kirkpatrick, Gelatt Jr. & Vecchi, Science (1983);
Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)]: one is the
simulated annealing method in which the temperature of the system is
controlled to search the global minimum; another is the quantum annealing
method which uses quantum effects." .
 Goto, Tatsumura & Dixon (Toshiba Corporation, Japan)
write in the Introduction of their paper
Science Advances (April, 2019) "...combinatorial optimization
problems ... are notoriously difficult
because of combinatorial explosion ...(& require) specialpurpose hardware
devices ... (like) "Ising Machines" ... . These machines have been developed
by various approaches: quantum computers based on quantum annealing
[Kadwaki & Nishimori, Physical Review E (1998); Das &
Chakrabarti, Reviews of Modern Physics (2008)]
or quantum adiabatic optimization [Farhi et al, arXiv/0001106 (2000);
Farhi et al., Science (2001); Albash & Lidar, Reviews of Modern Physics(2018)]
implemented with superconducting circuits [Johnson et al.,
Nature (2011); Boixo et al., Nature Physics (2014)] ... .".
***

