For a  brief and publicly edited version of my CV, see the Wikipedia entry.

Greetings! This is Bikas. My brief CV is as follows: Born in Dec. 1952, in Calcutta, to (Late) Bimal K. Chakrabarti and (Late) Pratima Chakrabarti. Got my Ph. D. Degree from Calcutta University in 1979. After that, I was post-doctoral 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 {SINP) as faculty in September 1983. A former director of SINP and at present INSA Senior Scientist at SINP (2021-), also Honorary Visiting Professor of economics (2007-) at the Indian Statistical Institute. I was Emeritus Professor of SINP and of S.N. Bose National Centre for Basic Sciences. Was awarded  S. S. Bhatnagar Prize (CSIR, India) in 1997 and was J. C. Bose National Fellow (DST, India)  for 2011-2020.  Married to Mrs. Kaberi Chakrabarti. Have two sons: Kalyan Sundar Chakrabarti and Anindya Sundar Chakrabarti.

I have professional interest in statistical physics, condensed matter physics, computational physics, and their application to social sciences.  See my papers, reviews or books. See  the (highlighted) last part of the entry "CITATIONS OF OUR WORK INCLUDE" for some typical recent  citations in this context.

RESEARCH:

Authored/co-authored more than 200 papers in refereed journals, 10 reviews [1 in Entropy, 1 in Eur. Phys. J. B, 2 in Frontiers in Physics, 2 in Phys. Rep. & 4 in Rev. Mod. Phys. , 10 books [3 Cambridge Univ. Press, 2 Oxford Univ. Press, 3 Springer, 2 Wiley-VCH].  For citations etc., see  Google Scholar and ResearchGate.

A FEW REPRESENTATIVE REVIEW PAPERS & BOOKS:

Review Papers : 

• • Statistics of Self-Avoiding Walks on Random Lattices (with K. Barat), Physics Reports (1995)

  • 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 Agent-Based Models (with A. Chakraborti,A. Chatterjee, D. Challet, M. Marsili & Y.-C. Zhang), Physics Reports (2015).

                                                                      &

Books :

• •  Quantum Ising Phases & Transitions in Transverse Ising Models (with A. Dutta & P. Sen), Springer, Heidelberg (1996)

  • Statistical Physics of Fracture & Breakdown in Disordered Systems (with L. G. Benguigui), Oxford Univ. Press, Oxford (1997)

  •  Econophysics: An Introduction (with A. Chakraborti, A. Chatterjee & S. Sinha), Wiley-VCH, Berlin (2010)

  • Quantum Ising Phases & Transitions in Transverse Ising Models (with J. -I. Inoue & S. Suzuki), Springer, Heidelberg (2013)

  • 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 (2015)

  • Statistical Physics of Fracture, Breakdown & Earthquake (with S. Biswas & P. Ray), Wiley-VCH, Berlin (2015).

  • Quantum Spin Glasses, Annealing and Computation (with S. Tanaka & R. Tamura), Cambridge Univ. Press, Cambridge & Delhi (2017)  [Contract signed between Morikita-Shuppan & CUP for Japanese Edition, 2017]

  • Econophysics of the Kolkata Restaurant Problem and Related Games:  Classical and Quantum Strategies for Multi-agent, Multi-choice 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)  * S. Mukherjee (2020).

Journal Editorial Board member of: ♦European Physical Journal B (past)  ♦ 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  (Past) ♦ Cambridge Elements in Econophysics  (with R N Mantegna, M Gallegati & I Vodenska)  (present) ♦   Statistical Physics of Fracture & Brekdown  (with P Ray), Wiley:   I, II, III, IV  (past) ♦  New Economic Windows series, Springer (present)

AWARDS & DISTINCTIONS:

Awards, Fellowships, etc

• • Young Scientist Award of INSA (1984)

  • Professeur Invité, University of Paris, UP13, Lab-PMTM, 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 (2016-2018) 

  • Honorary Emeritus Professor, S. N. Bose National Centre for Basic Sciences, Kolkata (2018- 2021)

  • INSA Scientist, Indian National Science Academy (2021 -)  

Peer Recognition/Appreciation

• •  “Influential” & “Elegant” papers from “Kolkata School”, Reviews of Modern Physics (2009) by Victor Yakovenko (Dept. Phys., Univ. Maryland) & J. Barkley Rosser Jr. (Dept. Econ., James Madison Univ.) [see pp. 1705, 1711 & throughout] 

  • "Father of Econophysics", Thesis (2018) by Christophe Schinckus, , Dept. History and Philosophy of Science, University of Cambridge [Open access, see pp. 15,16] 

  • "Earliest work in laying the foundation of Quantum Annealing",  Journal of Physics B (2022) by Helmut Ritsch et al., Inst. Theor. Phys., University of Innsbruck [Open access, see 3rd & 5th Paragraphs of the Introduction] 

  • "Adiabatic Quantum Computing"... "has attracted intense interest owing to its potential speedup over classical algorithms", PNAS (2023) by Frank Wilczek et al. from MIT & elsewhere [Open Access, see Abstract & 2nd paragraph of the paper] 

  • "Foundational paper": "25 years of random asset exchange modeling", European Physical Journal B (2024), by  Max Greenberg (Dept. Econ., University of Massachusetts Amherst)  & H. Oliver Gao (Dept. Systems Engg., Cornell University)  [Open access view only, see abstract & throughout] 

CONTACT:

E-mails: 

bikask.chakrabarti[at]saha.ac.in

bikask.chakrabarti[at]gmail.com

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CITATIONS OF OUR WORK INCLUDE:

REGARDING  ECONOPHYSICS & SOCIOPHYSICS:

♦ Discussions on "pioneering" papers from "Chakrabarti's research group" (p 187; pp 185-206) in the book 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 729-732, begins with  with the sentence  "According to Bikas Chakrabarti (...), the term 'econophysics' was neologized in 1995 at the second Statphys-Kolkata 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 in an entry by by  V M Yakovenko on "influential" papers (p. 2803) from "Kolkata School" (p. 2808; pp. 2800-2826; see also pp. 2792-2800) 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", says "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 real-world 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, Jean-Philippe 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. 73-78) 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 "Chakraborti-Chakrabarti model" as well as "Chatterjee-Chakrabarti-manna model" of income/wealth distributions in sections 5.3 (p. 167), 5.7 (pp. 205-210) 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 multi-agent 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 gamma-like, while (quenched) nonuniform saving propensity of the agents leads to a steady state distribution with a Pareto-like power-law 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. 75-76 and elsewhere. ♦  The book Macro-Econophysics, 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 the book   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 Thomson-Reuters ... 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."♦  The entry on Social Ontology in  The Stanford Encyclopedia of Philosophy (Stanford University, March 2018), writes "Social atomism (or atomistic individualism) holds that the social world is built out of individual people understood as isolated 'atoms' ...  The idea is to model societies as large aggregates of people, much as liquids and gases are aggregates of molecules, or ant colonies aggregates of ants. Historical examples include Quetelet’s 'On the Social System' of 1848 [Quetelet, Adolphe, 1848, Du système social et des lois qui le régissent, Paris: Guillaumin ] and Spencer 1895 [Spencer, Herbert, 1895, The Principles of Sociology, New York: Appleton]. Contemporary representatives include models in sociophysics and econophysics (see Chakrabarti et al. 2007 [Chakrabarti, Bikas K., Anirban Chakraborti and Arnab Chatterjee, 2007, Econophysics and Sociophysics: Trends and Perspectives, Hoboken, NJ: Wiley]). The simplest of these models take individual interactions to be governed by deterministic rules, and take a society or market to be an aggregate of these interacting individuals.".

♦ 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. 15-16) "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, Jean-Pierre 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 paper A simple and efficient kinetic model for wealth distribution with saving propensity effect, Physica A (September, 2020), Cui & Lin (School of Labor Economics, Capital Univ. of Economics and Business, Beijing; Sino-French Institute of Nuclear Engg.  & Tech., Sun Yat-Sen Univ., Zhuhai; Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua Univ., Beijing) write in the Abstract "The Lattice Gas Automaton (LGA) reduces to the simplest model with only random economic transaction if all agents are neighbors and no empty sites exist. The 1D-LGA has a higher computational efficiency than the 2D-LGA and [in] the famous Chakraborti–Chakrabarti economic model. ... With the increasing saving fraction, both the Gini coefficient and Kolkata index (for individual agents or two-earner families) reduce, while the deviation degree ... increases.".

♦♦ Our  book  Econophysics: An Introduction,  (with A. Chakraborti, A. Chatterjee & S. Sinha), Wiley-VCH, Berlin (2010) has been the only "Suggested Textbook" for the Econophysics courses  offered for the last twelve  years (since start of the program,  by Diego Garlaschelli)  at the Leiden University Physics Department,  where one of the first (1969)  Nobel Laureates in economics,  Jan Tinbergen, came from:

 ♦ Leiden Econophysics: 2012-2013            ♦  Leiden Econophysics: 2013-2014           ♦  Leiden Econophysics: 2014-2015

♦  Leiden Econophysics: 2015-2016            ♦  Leiden Econophysics: 2016-2017           ♦  Leiden Econophysics: 2017-2018  

♦  Leiden Econophysics: 2018-2019            ♦  Leiden Econophysics: 2019-2020           ♦  Leiden Econophysics: 2020-2021 

♦  Leiden Econophysics: 2021-2022            ♦  Leiden Econophysics: 2022-2023            ♦  Leiden Econophysics: 2023-2024            

♦  The "Kolkata Paise Restaurant Problem" was introduced in 2009  [Chakrabarti et al., Physica A (2009)] and in  2011, a Demonstration Project was launched  by  WOLFRAM Demonstrations.

♦ Ramzan (Dept. Physics,  Quaid-i-Azam University, Islamabad) in  Three-player quantum Kolkata restaurant problem under decoherence   (Quantum Information Processing, 2013) write in the Abstract "Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice’s payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice’s payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence (p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice’s payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.".

♦ Sharif & Heydari (Dept. Physics, Stockholm university, Stockholm) in their Quantum solution to a three player Kolkata restaurant problem using entangled qutrits  (Quantum Information & Computation, 2014;  arxiv: 1111.1962) write in the Abstract "Three player quantum Kolkata restaurant problem is modelled using three entangled qutrits. This first use of three level quantum states in this context is a step towards a N-choice generalization of the N-player quantum minority game. It is shown that a better than classical payoff is achieved by a Nash equilibrium solution where the space of available strategies is spanned by subsets of SU(3) and the players share a tripartite entangled initial state".

♦ Martin & Karaenke (Dept.  Informatics, Technical University of Munich, Munich) in their The Vehicle for Hire Problem: A Generalized Kolkata Paise Restaurant Problem  (2017) extend the problem  to that  of the mobile taxis  on hire by noting that the "... commercial drivers in  vehicle for hire markets (e.g., taxis, Uber, and Lyft) self-select their location and this could be the source of inefficiencies; i.e., drivers decide individually where to look for customers." and they modify such individual decisions to a an optimized one  by extending the (passive) role of the  "restaurants/taxis" vis-a-vis the choices of the customers.

♦  Kastampolidou, Papalitsas & Andronikos (Dept. Informatics, Ionian University, Greece) write in the Abstract of  their The Distributed Kolkata Paise Restaurant Game (Games, 2022) "The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this problem from a new angle and propose a novel strategy that results in greater utilization. Adopting a spatially distributed approach where the restaurants are uniformly distributed in the entire city area makes it possible for every agent to visit multiple restaurants. For each agent, the situation resembles that of the iconic traveling salesman, who must compute an optimal route through n cities. We rigorously prove probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The derived equations generalize formulas that were previously known in the literature, which can be seen as special cases of our results.". 

♦  Harlalka,  Belmonte  &  Griffin  (Dept. Comp. Sc.,  Dept. Maths.  & Applied Res. Lab., Penn State University,  Pennsylvania) write in the Abstract of their   Stability of dining clubs in the Kolkata Paise Restaurant Problem with and without cheating (Physica A,  2023) "We introduce the idea of a dining club to the Kolkata Paise Restaurant Problem. In this problem, N agents choose (randomly) among N restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in the dining club will coordinate their restaurant choice to avoid choice collision and increase their probability of eating. We model the problem of deciding whether to join the dining club as an evolutionary game and show that the strategy of joining the dining club is evolutionarily stable. We then introduce an optimized member tax to those individuals in the dining club, which is used to provide a safety net for those group members who do not eat because of collision with a non-dining club member. When non-dining club members are allowed to cheat and share communal food within the dining club, we show that a new unstable fixed point emerges in the dynamics. A bifurcation analysis is performed in this case. To conclude our theoretical study, we then introduce evolutionary dynamics for the cheater population and study these dynamics. Numerical experiments illustrate the behaviour of the system with more than one dining club and show several potential areas for future research.".

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REGARDING  QUANTUM ANNEALING & COMPUTATION (Selected few since 2014):

♦ Lucas (Lyman Laboratory of Physics, Dept.  Physics, Harvard University, Cambridge, MA)  in  (Frontiers in Physics, February 2014)  start his paper with the  sentences "Recently, there has been much interest in the possibility of using adiabatic quantum optimization  to solve NP-complete and NP-hard problems [Farhi et al., Science (2001); Das & Chakrabarti, Reviews of Modern Physics (2008)]. This is due to the following trick: suppose we have a quantum Hamiltonian HP whose ground state encodes the solution to a problem of interest, and another Hamiltonian H0, whose ground state is “easy” (both to find and to prepare in an experimental setup). Then, if we prepare a quantum system to be in the ground state of H0, and then adiabatically change the Hamiltonian for a time T according to   ...  then if T is large enough, and H0 and HP do not commute, the quantum system will remain in the ground state for all times, by the adiabatic theorem of quantum mechanics. At time T, measuring the quantum state will return a solution of our problem."  

♦ Boiixo et al. (Univ. S. California, ETH, ...) in their  Nature Physics, Vol. 10 (March 2014)  say "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)].

♦ 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 Aspuru-Guzik  (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; D-Wave 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.".

♦ 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 close-to-optimum solutions in many NP-hard 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 D-Wave [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 large-scale, albeit nonuniversal, quantum computation using present-day technology.". 

♦ 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 ...".

♦ 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 time-dependent 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).".

♦ Azinovic et al. (ETH Zurich; RIKEN, Wako-shi;  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 .".

♦ 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 single-spin- update Simulated Annealing (SA). This agrees with the intuition that a Stoquastic Adiabatic Quantum Computation 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 opening sentence "Quantum annealing aims at finding low-energy configurations of nonconvex optimization problems by a controlled quantum adiabatic evolution, where a time-dependent many-body 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)].".

♦ Dridi, Alghassi & Tayur (Quantum Computing Group, Carnegie Mellon Univ., USA) 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:  Science & Culture (May-June, 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 D-Wave 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 BC-17 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,  Japan) 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." .

♦ Albash & Hen (Dept. Physics & Quantum Info. Sc. Center, Univ. Southern California, USA) start their paper Science & Culture (May-June, 2019) with the sentences "Quantum annealing [Finnila et al., Chemical Physics Letters (1994); Brooke et al., Science (1999); Kadwaki & Nishimori, Physical Review E (1998); Farhi et al., Science (2001); Das & Chakrabarti, Reviews of Modern Physics (2008)] is a technique that utilizes gradually decreasing quantum fluctuations to search for global minima of complicated cost functions. As an inherently quantum technique, quantum annealing holds the promise to solve certain optimization problems faster than traditional classical algorithms as originally alluded to in the seminal paper of Ray, Chakrabarti & Chakrabarti [Physical Review B (1989)]."

♦ Schuetz et al. (Dept. Physics, Harvard Univ., USA, Centre for Quantum Physics, Univ. Innsbruck, Austria, Kavli Inst., Delft, Netherlands, Max Planck Inst., Garching, Germany) in their Physical Review B (June, 2019) write in the introduction "... we present a recipe to generate a targeted and scalable evolution for a large set of N qubits coupled via a single transmission line, thereby providing a natural architecture for the implementation of quantum algorithms, such as quantum annealing [Das & Chakrabarti, Reviews of Modern Physics (2008)] or the quantum approximate optimization algorithm [Farhi, Goldstone & Gutmann, arXiv:1411.4028 (2014); Farhi & Harrow, arXiv:1602.07674 (2016); Otterbach et al., arXiv:1712.05771 (2017)], designed to find approximate solutions to hard, combinatorial search problems.".

♦ Chang et al. (RIKEN, Saitama & Hyogo; Dept. Phys., Univ. California, Berkeley, USA, Lawrence Berkeley Nat. Lab., Berkeley, USA; Lawerence Livermore Nat. Lab, Livermore, USA; Quantum Comp. Inst., Oak Ridge Nat. Lab., Tennessee, USA) in their Scientific Reports (July, 2019) write "Akin to adiabatic quantum optimization [Farhi et al., arXiv:quantph/0001106 (2000)], quantum annealing prepares a quantum statistical distribution that approximates the solution by applying a slowly changing, time-dependent Hamiltonian [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Kadwaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews of Modern Physics, (2008)], where measurements drawn from the distribution represent candidate solutions. Unlike adiabatic quantum computing, quantum annealing permits non-adiabatic dynamics at non-zero temperature, making this approach easier to realize experimentally but also more challenging to distinguish quantum mechanically ...".

♦ Graß (Univ. Maryland, Maryland & Barcelona Institute of Sc. & Tech., Barcelona) begins his Physical Review Letters (September, 2019) with the opening sentences "Thanks to spectacular progress in controlling quantum systems, quantum dynamics has become a tool for solving hard computational problems. One strategy is quantum annealing  [Das & Chakrabarti, Reviews of Modern Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018); Hanke et al., arXiv: 1903.06559]: By incorporating the computational problem in the Hamiltonian, its solution is provided by the ground state which can be prepared by adiabatically reducing quantum fluctuations."

♦ Pearson et al.  (Univ. Southern California)  write in the Introduction of their paper  npj Quantum Information (November, 2019) "  ... to other forms of analog quantum computing [Das & Chakrabarti, Reviews of Modern Physics (2008)] ... Inspired by classical simulated annealing, in which thermal fluctuations are used to hop over barriers, quantum annealing uses quantum fluctuations to tunnel through barriers [Kadwaki & Nishimori, Physical Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)]; Brooke et al., Science (1999); Santoro et al., Science (2002); Boixo et al., Nature Commonication (2016); Muthukrishnan, Albash & Lidar, Physical Review X (2016); Denchev et al., Physical Review X (2017)].".

♦ Franzke and Kosko ( Department of Electrical & Computer Engineering, University of Southern California, Los Angeles), in their Physical Review E (November, 2019) write "Ray, Chakrabarti and Chakrabarti [Physical Review B (1989)] recast Kirkpatrick’s thermodynamic simulated annealing using quantum fluctuations to drive the state transitions.The resulting Quantum Annealing  algorithm uses a  transverse magnetic field in place of the temperature  in classical simulated annealing.".

♦ Martins (Faculty of Engineering, Univ. Porto, Porto)  in the thesis Applying Quantum Annealing to the Tail Assignment Problem (July, 2020), write in its Introduction "Based on the concept firstly presented by Ray, Chakrabarti & Chakrabarti [Physical Review B (1989)], Quantum Annealing  is a technique used for finding a global minimum of an objective function defined over an energy landscape using quantum mechanics [Kadowaki & Nishimori, Physical Review E (1998)]."

♦ Mills, Ronagh & Tamblyn (1QB Info. Tech., Vancouver; Univ. Ontario Inst. Tech., Ontario; Inst. Quantum Computing, Ontario; National Res. Council Canada, Ontario)  write in the introduction of their Nature Machine Intelligence (September, 2020), "When framed in the advent of quantum computation and quantum control, establishing robust and dynamic scheduling of control parameters becomes even more relevant. For example, the same optimization problems that can be cast as classical spin glasses are also amenable to quantum annealing [Farhi et al., Science (2001); Hen & Young, Physical Review A (2012); Boixo et al., Nature Physics (2014),  Bian et al, Frontiers in Physics (2014); Venturelli, Marchand, & Rojo, arXiv (2015)], exploiting, in lieu of thermal fluctuations, the phenomenon of quantum tunnelling [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Martoňák,  Santoro,  & Tosatti, Physical Review B (2002); Santoro et al., Science (2002)]  to escape local minima."

♦ Kerman (Linclon Lab,, MIT, Massachusetts)  starts his paper  Efficient numerical simulation of complex Josephson quantum circuits (arXiv, October, 2020), by saying "Superconducting quantum circuits built on the nonlinearity of Josephson junctions present an extraordinarily large design space, of which present-day device research has very likely only scratched the surface. ... so-called quantum annealing systems [Das & Chakrabarti, Reviews of Modern Physics (2008)] have been developed, based on flux qubits [...], which naturally emulate transverse field Ising spin models [...]." .

♦ Sanders et al. (Macquarie Univ., Sydney; Univ. Washington, Seattle;  Google Research, California,  ... ),  in their PRX Quantum (November, 2020), write in the Introduction "There are many prominent approaches to combinatorial optimization on a quantum computer. These include variants of Grover’s algorithm [Grover, Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC 96), New York (1996);  Durr & Hoyer,  arXiv:quant-ph/9607014 (1996)], quantum annealing [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Kadowaki & Nishimori, Physical Review E (1998)], adiabatic quantum computing [Farhi et al.,  arXiv:quantph/0001106 (2000);  Aharonov et al., SIAM Journal on Computing (2007)] ], ... ."

♦ Hauke, Mattiotti & Faccioli (Univ.  Trento, Trento) write in their Introduction of  Physical Review Letters (January, 2021) ,   "While significant progress has been made on designing algorithms for quantum annealers [Das &. Chakrabarti, Quantum Annealing and Related Optimization Methods, Springer (2005); Das & Chakrabarti, Reviews of Modern Physics (2008);  Albash & Lidar, Reviews of Modern Physics (2018); Venegas-Andraca, et al., Contemporary Physics (2018); Hauke et al, Reports on  Progress in Physics (2020)] that specifically tackle quantum chemistry applications [...] only a few applications to classical molecular sampling problems have been reported to this date [...] ... .".

♦ Alexeev et al., in the paper Quantum Computer Systems for Scientific Discovery ( PRX, February, 2021), based on a summary from a U.S. National Science Foundation workshop on Quantum Computing, prepared by a community of universities (including Caltech, Harvard Univ., MIT, Princeton Univ., Univ. California Berkeley, Univ. Chicago, Univ. Illinois Urbana-Champaign), national laboratories (including Argonne Nat. Lab., Sandia Nat. Lab., Nat. Inst. Standards and Tech.) , and industrial researchers (including Google, IBM T.J. Watson Res. Center, Microsoft Quantum), observe "The quantum computer promises enormous information storage and processing capacity that can eclipse any possible conventional computer ...  There are several known quantum algorithms that offer various advantages or speedups over classical computing approaches, some even reducing the complexity class of the problem." , &  make the comment "Quantum annealing models [Kadwaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews of Modern Physics (2008)] do not appear to be universal, and there is current debate over the advantage such models can have over classical computation [Rønnow et al., Science (2014)].".

♦ Song et al. (Korea Advanced Institution of Science and Technology, Daejeon) start their   Physisical Review Research (March, 2021) with the sentence "In recent years, quantum simulations have received significant attention because quantum annealing in particular has the potential to solve complex computational problems which are often intractable with nonquantum computational methods [Farhi et al., Science (2001); Das & Chakrabarti, Reviews of Modern  Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018); Hauke et al.,  Reports on Progress in Physics (2020)].".  

♦ Izquierdo et al. . (NASA Ames Research Center, California; USRA Research Institute for Advanced Computer Science, California), start their paper Physical Review Applied (April, 2021) with three sentences in the first paragraph: "Quantum computing provides novel mechanisms for efficient computing but the extent of its impact is as yet undetermined. A tantalizing area of application ... [is] quantum heuristics .. [which] have the potential to outperform these classical approaches. Here, we advance the understanding of one such heuristic, 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); Martonak, Santoro & Tosatti, Physical Review (2002); Santoro et al., Science (2002)], deepening the theoretical picture of ... the impact of annealing schedules and the interplay between quantum annealing parameters on performance, particularly on application-related problems that require embedding .".

♦  Sato, Ohzeki & Tanaka    ( Tohoku University, Sendai & Tokyo Institute of Technology, Tokyo)  start their paper    Scientific Reports, June, 2021  with the sentences  "Quantum annealing is an approach for solving combinatorial optimization problems starting form the quantum superpositioned state [Kadowaki & Nishimori, Physical Review E (1998)]. The quantum tunneling effect drives the system and searches the ground state in the rugged energy landscape [Ray,  Chakrabarti & Chakrabarti, Physical Review B (1989); Das, Chakrabarti & Stinchcombe, Physical  Review  E (2005); Das & Chakrabarti, Reviews of Modern Physics (2008); Morita & Nishimori, Journal of Mathematical Physics (2008); Masayuki, & Hidetoshi, Journal of Computation & Theoretical Neuro Science (2011)] .". 

♦ Campisi &  Buffoni (NEST, CNR & Scuola Normale Superiore, Pisa,  and  University of Florence, Florence)  write in their   Physisical Review E  (August, 2021),  "...  Without entering the details of what a quantum annealer is, how it works, and how it is used in  practice to solve optimization problems [Das & Chakrabarti, Reviews of Modern Physics (2008)], it suffices here to mention that a quantum annealer is a lattice of programmable superconducting qubits, with tunable interactions and local fields, which can be prepared and measured in a given eigen-basis. It thus implements a driven quantum spin network on a low-temperature microchip. ".

♦   Mohamed ( University of Waterloo, Ontario) in   Quantum Annealing: Research and Applications  (Thesis, 2021,  " Dedicated to All Women" )  write "Quantum Annealing (QA)  is similar to Simulated Annealing in the sense that the temperature parameter is analogous to the tunneling field strength in Quantum Annealing, since it exploits quantum tunneling on the quantum scale. The idea behind producing the quantum tunneling effect by a transverse field to help evolve the system into its ground state was first proposed in [Ray,  Chakrabarti & Chakrabarti, Physical Review B (1989) ].  ... QA performs a slow adiabatic process to let the initial ground state of the Hamiltonian evolve to the final ground state of the Hamiltonian that gives the desired solution of the problem [Das & Chakrabarti, Reviews of Modern Physics (2008)].". 

♦  Koshikawa et al. (Tohoku University, Sendai; Tokyo Institute of Technology, Tokyo; BMW Group, Tokyo; BMW Group, Munich) in  the Introduction of their    Combinatorial Black-box Optimization for Vehicle Design Problem (arXiv, October 2021)  write  "Quantum annealing (QA) is an approach for solving combinatorial optimization problems, starting from the quantum superposition state [Kadowaki & Nishimori, Physical Review E (1998)] . The quantum tunnelling effect drives the system and searches for the ground state (global minimum) in the rugged energy landscape  [Ray,  Chakrabarti & Chakrabarti, Physical Review B (1989);   Das,  Chakrabarti & Stinchcombe, Physical Review E (2005); Das & Chakrabarti, Reviews of Modern Physics (2008); Morita & Nishimori: Journal of Mathematical Physics (2008); Masayuki & Hidetoshi,  Journal of Computational and Theoretical Nanoscience (2011)].   The hardware implementation of QA has been developed by D-Wave Systems and performs at the production level, attracting much interest from academia and industry ...". 

♦   Sahimi & Tahmasebi ( Univ.  Southern California, California  & Univ Wyoming,  Laramie)  write in their   Physics Reports (October,  2021)  "It has been demonstrated that, in certain cases, particularly when the potential energy landscape consists of very high but thin energy barriers surrounding shallow local minima, the Quantum Annealing (QA) can outperform the Simulated Annealing  (SA). As discussed earlier, the transition probabilities in the SA are proportional to exp [−∆E/(kT) ] , which depend only on the magnitude ∆E of the barriers. If the barrier is very high, it is extremely difficult for thermal fluctuations in the SA to push the system out of such local minima. But, as argued by Ray et al. [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)], the quantum tunneling probability through  the same barrier depends not only on the height ∆E, but also on its width w and is approximately given by exp[−√(∆E)w/τ].  In the presence of quantum tunneling the additional factor w can be of great help in speeding up the computations, because if the barriers are thin enough, i.e., if w ≪ √(∆E), then quantum fluctuations can surely take the system out of the shallow local minima.  ... The method is most efficient for determining the ground states of glassy systems.  Ref. [Das & Chakrabarti, Reviews of Modern Physics (2008); Das & Chakrabarti (Eds.),   Quantum Annealing and Related Optimization Methods,  Lecture Notes in Physics, vol. 679, Springer (2005)] provide a good review of the QA.".

♦  Konz et al. ( ETH Zurich, Zurich; Univ. Innsbruck, Innsbruck; Amazon Quantum,   Washington; Microsoft Quantum, Washington)  start their paper   Embedding Overhead Scaling of Optimization Problems in Quantum Annealing  (PRX Quantum, November, 2021)  with the sentences "The availability of commercial quantum annealing devices [Johnson et al., Nature (2011);  Dickson et al., Nature Communication (2013); Bunyk et al.,  IEEE Transactions on Applied Superconductivity (2014)]    has revolutionized (quantum) optimization across many disciplines. The fruitful race [...]  between quantum optimization using quantum annealing [Finnila et al., Chemical Physics Letters  (1994);  Kadwaki &  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 and Related Optimization Methods, Eds.  A. Das & B. K. Chakrabarti, Lecture Notes in Physics, Springer (2005);  Santoro  &  Tosatti,  Topical  Review, Journal of Physics A (2006); Das & Chakrabarti, Reviews of Modern Physics (2008);  Morita & Nishimori, Journal of Mathematical Physics (2008); Hauke et al., Reports on Progress in Physics (2020)]  and classical algorithms on traditional CMOS hardware has resulted in multiple new ways to solve hard problems of practical importance previously thought to be intractable."

♦  Periwal et al. (Dept. Physics, Stanford University, California; SLAC National Accelerator Laboratory, California; Ludwig-Maximilians-Universität, Munich) write in the Abstract of their Nature (December, 2021) , "Typical interactions decay with distance and thus produce a network of connectivity governed by geometry, e.g., by the crystalline structure of a material or the trapping sites of atoms in a quantum simulator [Bloch, Dalibard & Nascimbene, Nature Physics (2012); Browaeys & Lahaye, Nature Physics (2020)]. However, many envisioned applications in quantum simulation and computation require richer coupling graphs including nonlocal interactions, which notably feature in mappings of hard optimization problems onto frustrated spin systems  [Das & Chakrabarti, Reviews of Modern Physics (2008); Gopalakrishnan, Lev, & Goldbart, Physical Review Letters (2011); Strack & S. Sachdev, Physical Review Letters (2011); McMahon et al., Science (2016); Berloff et al., Nature Materials (2017)] and in models of information scrambling in black holes [Hayden & Preskill, Journal of High Energy Physics (2007); Maldacena & Stanford, Physical Review D (2016); Bensten et al., Physical Review Letters (2019); Belyansky et al., Physical Review Letters (2020);].".

♦ Starchl  & Ritsch  (Inst. Theor.  Phys.,  Univ.  Innsbruck,  Austria)  write in the first few  paragraps of  their    Unraveling the origin of higher success probabilities in quantum annealing versus semi-classical annealing (January, 2022)   "Quantum computation has been proposed already in the early 80’s when Paul Benioff introduced a quantum Turing machine [Benioff, Journal of Statistical Physics (1980)], Feynman the universal quantum simulator [Feynman, Iternational Journal of Theoretical Physics (1982)],  and David Deutsch a universal circuit quantum computer [Deutsch, Proceedings of the Royal Society of London, Series A (1985)]. ... Most recently, strong claims have been put forward that quantum machines have solved sample problems not accessible to the best classical computers to date [Dowling & Milburn, Quantum Technology, The Second Quantum Revolution  (2002)].  ...  As full scale programmable quantum computers are technically extremely challenging to implement, many current efforts are devoted to adiabatic quantum simulation. Here one aims to prepare the ground state of a many-body Hamiltonian which encodes the solution to a classical optimization problem in tailored interactions [Das & Chakrabarti, Quantum Annealing & Related Optimisation Methods, Springer (2005)] ... Notably, one of the earliest work in laying the foundation of quantum annealing, was done in 1989 [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)], showing that quantum fluctuations can increase the ergodicity in a spin-glass model, by tunneling between ”trapping” minima, separated by narrow potential barriers. ... With a main focus on quantum annealing and analog quantum computation the review by Das et al. in 2008 [Das & Chakrabarti, Reviews of Modern Physics (2008)] gives an introduction to the initial progress of the subject matter and a clear picture of the fundamental physical properties and mechanisms of Quantum Annealing.". 

♦ Oshiyama and Ohzeki (Tohoku University, Sendai) start their Scientific Reports (February, 2022), with the sentence "Quantum annealing [Farhi et al., Science (2001); Das & Chakrabarti, Reviews of Modern Physics (2008)], which is a quantum algorithm for solving combinatorial optimization problems, has attracted a great deal of attention because it is implemented using real quantum systems by D-Wave Systems Inc. [Johnson et al., Nature (2011); Harris et al., Physical Review B (2010)] , aiming at becoming more powerful than classical algorithms such as simulated annealing [Kirkpatrick, Gelatt & Vecchi, Science (1983); Fu & Anderson, Journal of Physics A: Math & Gen. ((1986)].".

♦ Yaacoby et al.  (Weizmann Institute of Science, Rehovot; Technische Universität Berlin,  Berlin;  Ben-Gurion University, Beer-Sheva;  ASICTP, Trieste) write in  their   Physical Review E (March, 2022), "The physical motivation behind this suggestion is the ability of a quantum system to tunnel through energy barriers, which might offer a better channel to low-lying energy states, compared to classical thermal hopping. This approach of a heuristic algorithm whose purpose is to find an approximate ground state is known as quantum annealing [Das & Chakrabarti, Reviews of Modern Physics (2008)]. ...  Regaining ergodicity due to quantum fluctuations [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)] is therefore just a necessary condition that only ensures asymptotic convergence to the true ground state.".

♦ Yoon et al.(Los Alamos National Laboratory, Los Alamos; University of California, Berkeley; Lawrence Berkeley National Laboratory, Berkeley; ...) write in the Introduction  of their Scientific Reports (March, 2022),  "In contrast to the gate model quantum computation [Deutsch, Proceedings of the Royal Society London A (1989); Barenco, et al., Physical Review A (1995)], Adiabatic Quantum Computation performs an adiabatic time evolution from a ground state of a simple initial Hamiltonian to the state of the final Hamiltonian of the target problem [Farhi et al., arXiv: quant- ph/ 00011 06 (2000); Das & Chakrabarti, Reviews of Modern Physics (2008);  Albash & Lidar, Reviews of Modern Physics (2018)].  ... It solves combinatorial optimization problems using the quantum effect [of] tunneling through barriers between local minima [Ray, Chakrabarti & Chakrabarti,  Physical Review B (1989); Kadowaki & Nishimori, Physical Review E (1998); Santoro et al.,  Science (2002);  Mukherjee  & Chakrabarti, European Physical Journal Special Topics (2015)].".  

♦ Vuffray et al.  (Los Alamos National Laboratory, Los Alamos; Joint Quantum Institute, NIST/Univ. Maryland, Maryland) write in the Introduction of their PRX Quantum (April, 2022), "Adiabatic quantum computing [Farhi et al., Science  (2001)] exemplifies a promising physical principle that may lead to an enhanced exploration of the potentially rough energy landscape due to quantum tunneling [Das & Chakrabarti, Reviews of Modern Physics (2008)].  State-of-the-art quantum annealing processors [Johnson et al., Nature (2011)] were recently used to push the frontiers of quantum simulations [King et al., Nature (2018), Harris et al., Science (2018)], optimization [Mott et al., Nature (2017)], and machine learning [Amin et al., Physical Review X (2018)].".   

♦  Sinitsyn et al.  (Los Alamos National Laboratory,  Los Alamos)  start  their  papers  Physical Review Letters (November 2018)  and Nature Communications (April 2022)  with the sentences "Many optimization problems can be reformulated in terms of searching for a configuration that minimizes a Hamiltonian ... of ... Ising spins [Finnila et al.,  Chemical Physics Letters (1994); Santoro et al., Science (2002);  Das & Chakrabarti, Reviews of Modern Physics (2008)]. This  task is often so complex that it cannot be solved with modern computers. The idea of quantum annealing (QA) is to treat the Ising spins as z components of quantum spins ... and realize quantum evolution ..." and    "The ground state of a classical Ising spin Hamiltonian ... can be found after QA by mapping ... the projection Pauli operators of quantum spins-1/2 (qubits). The Hamiltonian for QA is generally defined  [Finnila et al.,  Chemical Physics Letters (1994); Kadwaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews of Modern Physics (2008); Hauke et a., Reports on Progress in Physics (2020)]  as ...  which means that many important QA problems that are usually formulated with a different ... target Hamiltonian, can be mapped to the model with only a polynomial overhead."  respectively. 

♦  Urushibata, Ohzeki & Tanaka (Tohoku University, Sendai; Tokyo Institute of Technology, Yokohama)  write  in  the Introduction of their    Journal of the Physical Society of Japan (June, 2022),   "Quantum annealing was originally proposed for solving optimization problems via  the quantum tunneling effect [Kadwaki &  Nishimori, Physical Review E (1998);  Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);  Das, Chakrabarti & Stinchcombe, Physical Review E (2005); Das & Chakrabarti, Reviews of Modern Physics (2008); Ohzeki &  Nishimori, Journal of Computational & Theoretical Nanoscience (2011)].". 

♦  Matsumori, Taki & Kadowaki  (DENSO CORPORATION,  Nisshin, Japan) start their   Scientific Report (July, 2022) with the sentences  "Computing algorithms and hardware that aim to solve a quadratic unconstrained binary optimization (QUBO) have been recently developed. Quantum annealing (QA) [Kadwaki &  Nishimori, Physical  Review E (1998) ; Das & Chakrabarti, Reviews of Modern Physics (2008)]  is one of the heuristic optimization algorithms for QUBO. QA utilizes quantum physics [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)]  to search for the optimal solution. QA is in the spotlight; after implementing QA in the quantum computer [Johnson et al., Nature (2011)], it was applied to some industry applications [Yarkoni et al.,  Quantum annealing for industry applications: Introduction and review. arXiv preprint arXiv: 2112.07491 (2021)].".

♦   Tennant et al. (Univ. Waterloo, Waterloo; MIT Lincoln Laboratory, Massachusetts; Univ. Southern California, California, ...)  write in the Introduction of their   npj Quantum Information (July 2022)   that  "Quantum annealing is emerging as a promising paradigm for near term quantum computing [Apolloni, Cesa-Bianchi, and  De Falco, Proceedings of Ascona/Locarno Conference (1988);  Das & Chakrabarti, Reviews of Modern Physics (2008); Hauke et al., Reports on Progress in Physics (2020); Albash and Lidar, Reviews of  Modern Physics (2018)]. An initial Hamiltonian, whose ground state is straightforward to prepare, is transformed continuously to the problem Hamiltonian. The prepared state of the problem Hamiltonian is located in the vicinity of the true groundstate and represents a useful solution of the optimization problem.".

♦  Harrington,  Mueller & Murch (MIT, Massachusetts; Cornell Univ., Ithaca;  Washington Univ., St. Louis), in the  Application section of their   Engineered dissipation for quantum information science, Nature Reviews Physics (August, 2022), write "While quantum simulation can involve “digital" approaches where the simulation is performed using gates on a quantum computer, engineered dissipation is most relevant for analog (or hybrid) approaches, where the degrees of freedom of the system-of-interest can map directly onto those of the physical hardware... .  For analog quantum simulation, dissipation engineering ... can be used to funnel quantum simulators into states of interest ... . The most familiar example of this is cooling, but there also exist protocols in which the dissipation is engineered to pump the system into a particular excited state ... . These same tools are also useful for annealing-based computational strategies [Das & Chakrabarti, Reviews of Modern Physics (2008)].".

♦ Nguyen et al.  (Harvard Univ., Massachusetts; Univ. Innsbruck, Innsbruck; Austrian Academy of Sciences, Innsbruck; ... )  start the Introduction of their arXiv (September, 2022) with the sentences "Combinatorial optimization seeks to find an optimal solution from a large set of discrete solutions, and has ubiquitous application in many areas of science and technology [Schrijver et al., Combinatorial optimization, Springer (2003);  Bernhard and Vygen, Combinatorial optimization, Springer (2008)]. Many such problems are known to be computationally hard for classical algorithms and fall into the NP-hard complexity class [Sipser, Introduction to the Theory of Computation, Course Technology (2013)]. The exploration of quantum speedup for solving these hard problems is one of the major topics in modern quantum information science. A variety of quantum algorithms such as quantum adiabatic algorithms [Farhi et al., arXiv:0001106 (2000); Farhi et al., Science (2001), Kadowaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews of Modern Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018)] and quantum approximate optimization algorithms [Farhi, Goldstone & Gutmann, arXiv:1411.4028 (2014)] have been proposed over the last two decades."

♦ Lau et al. (Centre for Quantum Technologies, National University of Singapore, Singapore) write in the  section on Quantum Annealing of their Review (addressed to general physicists  interested in the recent developments in quantum computing) NISQ computing: where are we  and where do we go?(AAPPS Bulletin, September 2022), "Introduced as the quantum analogue of simulated annealing [Kirkpatrick, Gelatt Jr. & Vecchi, Science (1983)],  quantum annealing  [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);  Finnila et al.,  Chemical Physics Letters (1994),  Das & Chakrabarti (eds.),  Quantum Annealing and Analog Quantum Computation,  Springer (2005)]  is a heuristic (no guarantees on quantum speedup) optimization algorithm that aims to solve complex optimization problems [Apolloni, Carvalho & De Falco,, Stochastic  Process & Applications (1989)]. This is done by encoding the solution of the problem into the ground state of what is called the annealer Hamiltonian [Kadowaki & Nishimori, Physical Review E (1998)] which is usually the transverse field Ising Hamiltonian, ...",             

♦ Yarkoni et al.  (Leiden University, Leiden; Honda Research Institute Europe) write in the Introduction of their Review on  Quantum Annealing for Industrial Applications (September, 2022), "The two leading paradigms are gate-based quantum computation (QC) and adiabati quantum computation (AQC) [Albash & Lidar, Reviews of Modern Physics (2018); Das & Chakrabarti, Reviews of Modern Physics (2008);  Farhi et al., Technical Report MIT-CTP-2936 (2000); Hauke  et al., Reports on Progress in Physics  (2020); Morita & Nishimori, Journal of Mathematical Physics (2008)]. ... An approach closely related to AQC is quantum annealing (QA)  [Das & Chakrabarti, Reviews of Modern Physics (2008);  Hauke  et al., Reports on Progress in Physics  (2020); McGeoch,  Synthesis Lectures on Quantum Computing (2014); Morita & Nishimori, Journal of Mathematical Physics (2008); Tanaka, Tamura & Chakrabarti, Quantum Spin Glasses, Annealing and Computation Cambridge Univ. Press (2017)], proposed in 1988 by Apolloni et al. [Apolloni, Cesabianchi & De Falco, International Conference on Stochastic Processes (1988)]." 

♦ Ghamari et al.,  (Univ. of Trento, Trento; Frankfurt Institute for Advanced Studies, Frankfurt)  write in the Introduction of their Scientific Report (September, 2022), "Then, Quntum Computing  on a quantum annealing machine [Das & Chakrabarti (eds.),  Quantum Annealing and Analog Quantum Computation,  Springer (2005); Das & Chakrabarti, Reviews of Modern Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018); Venegas-Andraca et al, Contemporary Physics (2018); Hauke  et al., Reports on Progress in Physics  (2020)] generates transition paths connecting the previously generated configurations. These paths are then accepted or rejected according to a Metropolis criterion implemented on a classical computer, which combines the statistical mechanics of the transition path ensemble with the internal physics of the quantum annealing machine, for which we used the D-Wave machine [Inc., D.-Wave Systems Leap webpage (2022)].".       

♦  Woo et al.,  (Seoul National University, Seoul) write in the section on Theoretical model of probilistic-computing of their Nature Communications (September, 2022) "Quantum annealing is based on an energy-based model to solve combinatorial optimization problems. In quantum annealing, the energy of a quantum system comprised of “qubits” is defined as Hamiltonians, further divided into the initial and final Hamiltonian. The initial Hamiltonian denotes the initial ground state of the system, where each qubit remains in a state with the quantum superposition of 0 and 1. As the system undergoes the annealing procedure, the initial Hamiltonian slowly develops into the final Hamiltonian, which provides a low-energy solution to the given problem [Das & Chakrabarti, Reviews of Modern Physics (2008)].". 

♦ Tasseff et al. (Los Alamos National Laboratory, Los Alamos; University of New Mexico, Albuquerque), start the  Introduction of their arXiv (October, 2022), with the sentences "In the 1990s, an optimization algorithm called quantum annealing (QA) was proposed with the aim of providing a fast heuristic for solving combinatorial optimization problems [Kadowaki & Nishimori, Physical Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);  Finnila et al.,  Chemical Physics Letters (1994); Farhi et al., Science  (2001);  Santoro et al., Science (2002)]. At a high level, QA is an analog quantum algorithm that leverages the non-classical properties of quantum systems and continuous time evolution to minimize a discrete function.   ...   Although this work demonstrates encouraging results for the QA computing model, we also emphasize that it does not provide evidence of a fundamental or irrefutable performance benefit for this technology. ...  We look forward to and encourage ongoing research into benchmarking the QA computing model, as closing the performance gap presented in this work would provide significant algorithmic insights into heuristic optimization methods, benefiting a variety of practical optimization tasks. " .     

♦ Hegade, Chen & Solano  (Shanghai Univ., Shanghai, Univ. of  Basque Country, Bilbao,  Kipu Quantum,  Munich) start the  Introduction of their  Physical Review Research (November, 2022) with the sentences,  "Many important optimization problems in science and industry can be formulated as solving combinatorial optimization problems [Fu & Anderson, Journal of Physics A (1986)].  In general, these problems are known to be NP-hard so that no classical or quantum computers are expected to solve them efficiently. However, there is a hope that quantum computers might give some polynomial speedup, which helps reduce the resources and, hence, the cost of solving many practical problems of interest. Especially, adiabatic quantum optimization algorithms are developed to tackle such problems [Farhi et al, Science (2001); Das & Chakrabarti, Reviews of Modern Physics (2008), Albash & Lidar, Reviews of Modern Physics (2018)].".

♦ Schindler ... Demler, Cirac et al. (Max-Planck-Institute, Dresden & Garching;  Freie Universität Berlin, Berlin; Chinese Academy of Sciences,  Beijing; ETH Zurich, Zurich) show in their  Physical Review Letters  (November, 2022) for the investigation on  ground state(s)  of the quantum Sherringtoin-Kirkpatrick model (at zero temperature), in  the context of the "evidence that the quantumness can be exploited to shortcut optimization tasks, for instance, through quantum annealing," that  the conjecture for the exstence of the  "quantum de Almeida–Thouless line in the model [Young, Physical Review E (2017);  Manai & Warzel, Journal of Statistical Physics (2022)], suggesting the existence of a line of quantum phase transitions between the spin glass and paramagnetic phases that extends from the (critical transverse field) g_c  and (longitudinal field)  h =  0 critical point into the h > 0 plane", which is based on "not yet conclusive investigations of the stability of Replica Symmetry Breaking (RSB) at zero temperature" is untenable. "Our variational analysis can tackle this issue without  making assumptions about RSB. Indeed, we can extend our  analysis to variational ground states in the whole parameter space of the model, including h > 0. We observe that all indicators of a phase transition vanish as soon as h > 0". This finding confirms the earlier extensive numerical observations, using finite temperature Monte Carlo for the effective Suzuki-Trotter Hamitonian and exact diagonalization for the model reported in  "[Ray, Chakrabarti, Chakrabarti, Physical Review B (1989); Chakrabarti, Dutta & Sen, Quantum Ising Phases and Transitions in Transverse Ising Models, Springer, New York (1996);  Sen, Ray & Chakrabarti, arXiv:cond-mat/9705297 (1997); Das & Chakrabarti, Physical Review E (2008); Mukherjee, Rajak & Chakrabarti, Physical Review E (2015); Mukherjee, Rajak & Chakrabarti, Physical Review E (2018)]". 

♦ Unanyan, Vitanov & Fleischhauer (Technische Universitat Kaiserslautern,  Kaiserslautern;  St Kliment Ohridski Univ. of Sofia, Sofia) write in the Introduction of their  Journal of Physics B: Atomic, Molecular & Optical Physics (January, 2023), "Finally, the success of adiabatic quantum control techniques over the last decades has triggered the emergence of an entirely new concept in quantum information: adiabatic quantum computation and quantum simulation [Farhi et al., arXiv:quant-ph/0001106 (2000); Das & Chakrabarti, Reviews of Modern Physics (2008)].".    

♦ Trey (Treyquantum@gmail.com) write in the Introduction of  Quantum Annealing for Subset Product  (January, 2023), "Quantum annealing was originated from Ray, Chakrabarti & Chakrabarti, Physical Review B (1989), where quantum fluctuations were found to be helpful for finding the lowest energy state of Ising spin glasses; and it is formulated in Kadowaki & Nishimori, Physical Review E (1998), where quantum fluctuations were introduced into simulated annealing."  &  Okuyama1 and Ohzeki (Tohoku University, Sendai;  Tokyo Institute of Technology, Tokyo)  start the Introduction of their Threshold theorem in quantum annealing with deterministic analog control errors (January, 2023) with the sentence  "Quantum annealing [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); Farhi et al. arXiv: quant-ph/0001106 (2001); Aharonov et al., SIAM Journal of Computing (2007); Mizel,  Lidar & Mitchell, Physical Review Letters (2007)] is an analog quantum computation that utilizes continuous time evolution of quantum systems, and, thereby, analog control errors of the parameters are inevitable in experimental systems.".

♦ Au-Yeung, Chancellor & Halffmann (Univ. Strathclyde, Glasgow; Durham Univ. , Durham;  Fraunhofer Institute of Industrial Mathematics, Fraunhofer) write in the Abstract of their Frontiers in Physics (February, 2023), "In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor’s algorithm through experiments to the era of noisy intermediate scale quantum devices for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-)hard optimization problems where classical approaches fail." and write in the Introduction "The aim of this perspective is to critically examine the status and future of quantum computing for optimization, which we define as quantum optimization, including some possible weaknesses. We intend to complement the Royal Society’s recent special edition on quantum annealing [Chakrabarti et al., Philosophical Transactions of the Royal Society A (2023)] and Applied Quantum Computing’s excellent review which provides accessible explanations for the technicalities of quantum computing and their practical uses [Cumming & Thomas, arXiv 2211.13080]." 

♦ Nguyen et al. (Harvard University,  Massachusetts;  University of Innsbruck, Innsbruck; ...)  start  the Introduction of their PRX QUANTUM (February,  2023) with the sentences "Quantum optimization ... solve ...  by utilizing controlled dynamics of quantum many-body systems. The key idea underlying this paradigm is to steer the dynamics of quantum systems such that their final states provide solutions to the optimization problem of interest. Such dynamics are often achieved either via the adiabatic principle in quantum annealing algorithms  [Farhi et al., arXiv:0001106 (2000); Farhi et al., Science (2001); Kadowaki & Nishimori, Physical Review E (1998);  Das & Chakrabarti, Reviews of Modern Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018)], or by employing more general, variational approaches, as exemplified by quantum approximate optimization algorithms [Farhi, Goldstone & Gutmann,  arXiv:1411.4028 (2014)].". 

♦ Wienberg et al. (QC Ware Corp., Palo Alto, California; Aisin Corp., Tokyo Research Center, Tokyo; Aisin Technical Center of America,  California)  write in the  Introduction of their Supply chain logistics with quantum and classical annealing algorithms (Scientific Reports, March 2023), "Quantum annealing attempts to use quantum tunneling through energy landscapes to more efficiently reach global low-energy states that represent the minimum of an optimization problem [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Motita & Nishimori, Journal of Physics A: Math. Gen. (2006); Das & Chakrabarti, Reviews of Modern Physics (2008); Albash & Lidar, Reviews of Modern Physics (2018); King et al., Journal of Physical Society of Japan (2019). And D-Wave Systems offers quantum annealing hardware that can optimize Quadratic Unconstrained Binary Optimization  instances with thousands of variables already.

♦ Wierzbinski, Falco‑Roget & Crimi (Institute of Mathematics, University of Warsaw, Warsaw; Sano Center for Compuational Personalised Medicine, Krakow ) write in the Abstract of their Scientific Reports (March, 2023), "Recent advancements in network neuroscience are pointing in the direction of considering the brain as a small-world system with an efficient integration-segregation balance that facilitates different cognitive tasks and functions. In this context, community detection is a pivotal issue in computational neuroscience. In this paper we explored community detection within brain connectomes using the power of quantum annealers ... ", and write in the Introduction "Optimization problems in quantum devices ... exploitable for Simulated Annealing [Guimera, Sales-Pardo & Amaral,  Physical Review E (2004)]   as well as its quantum partner, namely Quantum annealing  algorithms [Farhi et al., Science (2001)] (but see also a comprehensive review [Rajak et al., Philosophical Transactions of the Royal Society A (2023)]). ". 

♦ Albertsson & Rusu  (KTH Royal Institute of Technology,  Kista, Sweden)  start their their  Scientific Report (March, 2023) with the sentences "Unconventional computing paradigms based on natural processes have recently inspired the development of various hardware architectures, which can potentially outperform conventional Von-Neuman architectures for various applications, ... Ising Machines  belong to the class of architectures that employs the Ising Model for solving optimization problems.  The most widely known Ising Machines  are quantum annealers [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Apolloni, Carvalho & de Falco, Stochastic Processes & Applications (1989); Kadowaki & Nishimori, Physical Review E (1998)], which are currently commercially available by D-Wave [McGeoch & Farré,  Advantage processor overview (2022)]. These systems are based on coupled Josephson junctions and have shown promising results as the first step to quantum computing [Johnson et al., Nature (2011)]. ".

♦ Menendez, Bello & Clark  (Zurich Research Laboratory, IBM Quantum, Zurich; King's College London; University College London) start  the Introduction of their paper in the  Proc. 4th International Workshop on Quantum Software Engineering: Q-SE 2023 (March, 2023) with the sentences "This new decade is bringing remarkable steps forward in terms of computation. One of the most relevant is quantum computers, new systems that leverage the power of quantum mechanics to solve complex problems that can be encoded in a probabilistic framework. ... One such step forward is the possibility of implementing new efficient quantum algorithms that deal with classical computational problems, such as Shor’s algorithm for factorisation [Lanyon et al., Physical Review Letters (2007)], Grover’s algorithm for search problems [Grassl et al., in Post-Quantum Cryptography, Springer (2016)] and Quantum Annealing algorithms for optimisation [Das & Chakrabarti, Reviews of Modern Physics (2008)].".

♦  Morrell et al.,  (Los Alamos National Laboratory, New Mexico;  Univ. New Mexico, New Mexico) start their  Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing (Physical Review Applied, March, 2023)  with the sentance  "Quantum annealing is an analog computing approach for preparing low-energy eigenstates of classical and quantum Hamiltonians [Finnila et al.,  Chemical Physics Letters (1994); Kadwaki &  Nishimori, Physical  Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Santoro et al., Science (2002)]. At the heart of the algorithm is the Adiabatic Theorem [Born & Fock, Zeitschrift f ̈ur Physik  (1928); Kato, Journal of the Physical Society of Japan (1950); Jansen, Ruskai, & Seiler, Journal of Mathematical Physics (2007)], which guarantees that a quantum system initially prepared in the ground state of a time-evolving Hamiltonian will remain with high probability in the instantaneous ground state at later times as long as the evolution satisfies an adiabatic condition. Quantum annealing exploits this property by slowly interpolating between a Hamiltonian for which the ground state is known and a target Hamiltonian that we wish to minimize [Finnila et al.,  Chemical Physics Letters (1994); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Santoro et al., Science (2002)]. An advantage of quantum annealing over gate-based implementations of quantum computation is its minimal control requirements ... generically, the qubits are annealed uniformly and slowly, which in principle makes it readily scalable to thousands of qubits. For this reason, quantum annealing remains a promising quantum optimization metaheuristic in the noisy intermediate-scale quantum era [Preskill, Quantum  (2018)] ... However, just like any other analog computing method, quantum annealing is sensitive to hardware defects, limited controller accuracy ... that are inherently present in any physical system."

♦ Ceselli & Premoli  (Dept. Comp. Sc.,  Univ. of  Milan, Milan) start  their Scientific Reports (April, 2023), with the sentences "Dedicated hardware performing quantum annealing (QA) is currently available and steadily improving [Bunyk et al., IEEE Transactions on Applied Superconductivity  (2014); Johnson  et al.,  Nature (2011)]. QA was independently proposed and refined multiple times [Frahi et al., Science (2001),  Apolloni et al.,  Stochastic Processes, Physics and Geometry: Proc.  Ascona-Locarno Conf. (1990); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)] and is based on the principles of adiabatic quantum computation [Albash & Lidar,  Reviews of Modern Physics (2018),  McGeoch,  Synthesis Lectures on Quantum Computing (2014);  Das & Chakrabarti, Reviews of Modern Physics (2008)].  The agreed present formulation of QA was introduced by Kadowaki and Nishimori [Physical  Review E (1998)]." . 

♦ Pelofske, Hahn & Djidjev (Los Alamos National Laboratory, Los Alamos; Harvard T H Chan School of Public Health, Boston; Bulgarian Academy of Sciences, Sofia) start their Quantum Science & Technology (April, 2023) with the sentences "Quantum annealing   is a novel computing technology that uses quantum fluctuations to search for a global minimum of a combinatorial optimization problem  [Das & Chakrabarti, Reviews of Modern Physics (2008); Finniala et al., Chemical Physics Letters (1994); Hauke et al. , Reports on Progress in Physics (2020); Johnson et al., Nature (2018); Kadowaki & Nishimori, Physical Review E (1998); Lanting et al., Physical Review X (2014); Morita & Nishimori, Journal of Mathematical Physics (2008); Ohkuwa, Nishimori & Lidar, Physical Review A (2018)]. The quantum annealers manufactured by D-Wave Systems, Inc., are specialized hardware devices that implement quantum annealing.".     

♦ Richoux, Baffier & Codognet (CNRS, Sorbonne University, Paris &  University of Tokyo, Tokyo) introduce Qauantum Annealing (QA) in  their Document (April, 2023) saying "QA has been proposed as a concrete form of adiabatic computation more than two decades ago by Kadowaki & Nishimori [Physical Review E (1998)] and Farhi et al. [Science (2001)], and takes advantage of the physical phenomenon of quantum tunneling, allowing to traverse energy barriers in the energy landscape as long as they are not too large [Tanaka, Tamura & Chakrabarti, Quantum Spin Glasses, Annealing & Computation, Cambridge University Press (2017); Rajak et al., Philosophical Transactions of the Royal Society A (2023)]. QA has gained momentum in the last decade with the development of special hardware based on QA, such as the quantum computers of D-Wave Systems [Bunyk et al., IEEE Transactions on Applied Superconductivity (2014); McGeoch et al., Computer (2016)] and, more recently, the so-called “quantum-inspired” systems which are realized with classical (non-quantum) electronics by Fujitsu [Aramon et al., Frontiers in Physics (2019)], Hitachi [Yamaoka et al., Proc. IEEE Custom Integrated Circuits Conference, Austin (2019)], Toshiba [Goto, Tatsumura & Dixon,  Science Advances (2019)] or Fixstars Amplify [Matsuda, 2020 IEICE General Conference (2020)].".

♦ King et al (D-Wave Systems, British Columbia;  Boston University,  Massachusetts; Simon Fraser University, British Columbia) begin the Abstract  of their Nature (April, 2023) with the sentence  "Experiments on disordered alloys  [Brooke et al., Science (1999); Aeppli & T. F. Rosenbaum, in Quantum Annealing and Other Optimization Methods, eds. Das & Chakrabarti, Springer (2005); Das & Chakrabarti, Reviews of Modern Physics (2008)] suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing.", and write in their Introduction "... Thus originated Quantum Annealing (QA) as a means of both studying quantum critical phenomena and optimizing quadratic objective functions [Albash & Lidar, Reviews of Modern Physics (2018);  Das & Chakrabarti, Eds., Quantum Annealing and Other Optimization Methods, Springer (2005)].".

♦ Hasegawa, Oshiyama & Ohzeki (Tohoku University, Sendai; Tokyo Institute of Technology, Tokyo; ...)  start their Kernel Learning by quantum annealer (arXiv, April 2023) with the sentences "Quantum annealing is a heuristic algorithm that searches for the ground state of a predetermined Hamiltonian by using quantum tunneling effects [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);  Kadowaki & Nishimori, Physical Review E (1998)]. It has been used in numerous applications [Yarkoni et al., Reports on Progress in Physics (2022)], including portfolio optimization [Rosenberg et al. (2016); Venturelli et al. (2019)], molecular similarity problem [Hernande et al. (2017)] quantum chemical calculation [Streif et al, (2019)], scheduling problem [Venturelli et al. (2016); Ikeda et al. (2019); Yarkoni et al. (2021)], traffic optimization [Stollenwerk et al. (2020); Inoue et al. (2021)], machine learning [Neven et al. (2009);  Macready et al. (2010); Neukart et al. (2018); Crawford et al. (2019); Sato et al. (2021)], web recommendation [Nishimura et al. (2019)], and route optimization for automated guided vehicles in factories [Ohzeki et al. (2019); Haba et al. (2022)], as well as in decoding problems [Ide et al. (2020); Arai et al. (2021)].".

♦ Serrano et al. (Computer Science, University of Castilla-La Mancha. Spain;  Computer Science, University of Bari Aldo Moro, Italy.) write in  their Software Quality Journal  (May, 2023)  "Quantum Leap from quantum computer manufacturer D-Wave provide optimization environments for NP-hard combinatorial problems using adiabatic quantum optimization [Farhi et al., Science ( 2001); Das & Chakrabarti,  Reviews of Modern Physics (2008)].".

♦ Zielinski et al. (Ludwig Maximilian University,  Munich; Delft University of Technology, Delft) write in the Introduction of their arXiv (May,  2023) "Quantum Annealing is a heuristic approach to solve combinatorial optimization problems. It may be seen as a variation of the more common simulated annealing  metaheuristic [McGeoch, Adiabatic quantum computation and quantum annealing: Theory and practice, Synthesis Lectures on Quantum Computing (2014)] . The idea of incorporating quantum phenomena rather than thermal annealing into a heuristic optimization framework appears to have been independently suggested by several researchers [Apolloni, Cesa-Bianchi & De Falco, Stochastic Processes, Physics & Geometry: Proceedings of the Ascona-Locarno Conference (1990); Farhi et al, Science (2001); Kadowaki & Nishimori, Physical Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)]. Commercially available quantum annealers are  currently produced by company D-Wave Systems.".

♦  Yin, ... Wilczek (Corresponding author) et al. (Theoretical Physics, MIT, Cambridge;  University of Science and Technology of China, Hefei; Peking University, Beijing; Wilczek Quantum Center, Shanghai Jiao Tong University, Shanghai; Stockholm University, Stockholm;  Arizona State University, Arizona) start the 'Abstract' of their  Proceedings of the National Academy of Science USA (May, 2023) with the sentences  "An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472–475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061–1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian H_IS[G(V,E)], with edges E being the two-body interactions between adjacent vertices V. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of H_IS[G(V,E)]."  and claim in the 'Significance', "Our work opens an avenue of quantum computation, which will undoubtedly bring near-term practical applications.".  

♦  Wang et al.  (Peking University, Beijing ; Shanghai Jiao Tong University, Shanghai; ...) write in their  Physical Review Research (June 2023)  "In Ref.  [Farhi,  Goldstone & Gutmann,  arXiv:1411.4028 (2014)], the original setup is inspired by a quantum adiabatic (annealing) algorithm [Kadowaki & Nishimori, Physical Review E (1998);  Aharonov et al., SIAM Journal on  Computing,  (2007);  Das & Chakrabarti, Reviews of  Modern  Physics (2008)] such that ...".

♦ Xiong  et al.  (Inst. Nano-Devices & Quantum Computing, Fudan University, Shanghai;  Huawei Computing Technologies, Shenzhen;  ...) write in the Introduction of their  Q-Drug: Drug Design into Quantum Space using Deep  Learning  (arXiv, August  2023), "Quantum annealing is a discrete optimization process that uses quantum fluctuation characteristics and can find the global optimal solution when the objective function has many candidate solutions. The theory of quantum annealing dates back to 1989 when Ray et al. proposed that quantum tunneling could help escape from the local minima of classical Ising spin glasses with rugged energy landscapes  [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)]. The advantages of quantum annealing were verified in numerical tests in 1998 [Kadowaki & Nishimori, Physical Review E (1998)],  and in 1999, the first experiments on quantum annealing in LiHoYF Ising glass magnets were conducted [Brooke et al., Science (1999)]. D-Wave Systems marketed a quantum annealing machine built on superconducting circuits in 2011 [Johnson et al., Nature (2011)],  and over the last decade, superconducting circuit-based and laser pulse-based quantum annealing machines have advanced rapidly with more qubits and better connections [...]."         

♦ Koniorczyk et al.  (Wigner Research Centre for Physics, Budapest; Technical University of Dresden, Dresden; Polish Academy of Sciences, Gliwice; ... ) write in the section on "Quantum annealing and its applications" of their  Application of a Hybrid Algorithm Based on Quantum Annealing to Solve a Metropolitan Scale Railway Dispatching Problem (arXiv, September 2023),  "Quantum annealing [A. Das & B. K. Chakrabarti, Reviews of Modern Physics (2008)] is an optimisation method analogous to simulated annealing. Both can be used for the unconstrained minimisation of a quadratic function of ±1-valued variables, which represents the energy configuration for a set of spins of the Ising model [E. Ising, “Beitrag zur theorie des ferromagnetismus,” Z. Physik, vol. 31, pp. 253–258 (1925), https://doi.org/10.1007/bf02980577; Z. Bian,  F. Chudak, W. G. Macready, & G. Rose*, “The Ising model: teaching an old problem new tricks,” D-wave systems, vol. 2, pp. 1-32 (2010)]; an important and celebrated problem in physics."  [*G. Rose, Founder of D-Wave Systems Quantum Annealers]. 

♦ Abel, Nutricati & Rizos  (Theor. Phys.,  CERN, Geneva, Phys. & Maths, Durham University, Durham; Phys.,  University of Ioannina, Ioannina) write in the Abstract of  their  String Model Building on Quantum Annealers (Wiley Online Library, Sept. 2023)  "For the first time the direct construction of string models on quantum annealers has been explored and has been investigated their efficiency and effectiveness in the model discovery process. Through a thorough comparison with traditional methods such as simulated annealing, random scans, and genetic algorithms, it is highlighted the potential advantages offered by quantum annealers, which in this study promised to be roughly 50 times faster than random scans and genetic algorithm and approximately four times faster than simulated annealing.", and write in the Introduction "In this paper we shall consider a different class of heuristic search method in the string context, namely quantum adiabatic algorithms [Farhi et al., arXiv: quant-ph/0001106 (2000); Das & Chakrabarti, Quantum Annealing and Related Optimization Methods, Springer, Berlin (2005)].".

♦  Kerger & Miyazaki   (Dept. Appl. Maths & Stat., Johns Hopkins University, Maryland; NASA Ames Research Center, California; Research Inst.  Adv. Comp. Sc., Universities Space Research Association, California; NEC Corporation, Kawasaki & Tsukuba) start the Introduction of their Quantum image denoising: a framework via Boltzmann machines, QUBO, and quantum annealing (Front. Comp. Sc., Oct., 20023 with the sentences "Quantum Annealing (QA)  [Kadowaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews  of Modern Physics  (2008); Albash & Lidar, Reviews of Modern Physics (2018)] is a promising technology for obtaining good solutions to difficult optimization problems, by making use of quantum interactions to aim to solve Ising or quadratic unconstrained binary optimization (QUBO) instances. Since Ising and QUBO instances are NP-hard, and many other combinatorial optimization problems can be reformulated as Ising or QUBO instances [see e.g., Glover, Kochenberger & Du, 4OR-Q Journal of Operearations Research (2019)], QA has the potential to become an extremely useful tool for optimization."

♦ Dubey & Hein (University of Luxembourg, Luxembourg) write in the Introduction on Quantum Annealing (QA) in their  Satellite Routing with Quantum Annealing: Collecting Space Debris and On-orbit Servicing (October 2023), "The recent advancements in the manipulation of quantum states have given rise to the concept of quantum computation and simulation. Initially rooted in theoretical concepts, this notion has now expanded to promote an established sector with vast potential for technological applications [Rajak et al., Philosophical Transactions of the Royal Society A (2023)].  ... The development and subsequent commercialization of a superconducting circuit quantum Ising glass annealing machine was achieved by D-wave systems [Johnson et al., Nature (2011)]. Subsequently, significant transformation has occurred as a result of a proliferation of remarkable research papers in both theoretical and experimental domains. ... There are several literature which presents an overview of the QA based protocol and delves into recent theoretical and experimental advancements in QA that leverage the benefits of quantum tunneling for identifying the minimum of a classical energy function [Rajak et al., Philosophical Transactions of the Royal Society A (2023); Mukherjee, Philosophical Transactions of the Royal Society A (2023); Chakrabarti et al.,  Philosophical Transactions of the Royal Society A (2023)]."

♦   Pelofske, Hahn & Djidjev  (Los Alamos National Laboratory, Los Alamos; Harvard School of Public Health, Harvard University, Boston;  ...) start their  IEEE Transactions on Quantum Engineering (November 2023) with the sentences  "Quantum annealing  is a form of specialized quantum computation that uses quantum fluctuations in order to search for the global minimum of a combinatorial optimization problem [Kadowaki & Nishimori, Physical Review E (1998); Das & Chakrabarti, Reviews  of Modern Physics  (2008); Morita & Nishimori, Jounal of Mathematical Physics (2008); Hauke et al., Reports on Progress in Physics (2000) ; Farhi et al., arXiv: quant-ph/0001106 (2000); Chakrabarti et al., Philosophical Transactions of the Royal Society A (2023)]. Programmable quantum annealers, available as cloud computing resources, are manufactured by D-Wave Systems, Inc., using superconducting flux qubits [Johnson et al., Nature (2011); Lanting et al.,  Physical Review X (2014); Boixo et al, Nature Communication (2013); Boixo et al., Nature Physics (2014); Mandra et al., Physical Review A (2016); King et al., Nature Physics (2022)].".

♦ Bastidas  et al.  (NTT Research, Laboratories,  Kanagawa & California;  Dept. Phys., Harvard University, Massachusetts;  Dept.  Phys., Massachusetts Institute of Technology, Massachusetts)  write in the Introduction of  their Physical Review B (January, 2024)  "Indeed, most explorations into the nonequilibrium behavior of condensed matter systems [Polkovnikov et al., Reviews of Modern Physics (2011);  Hatomura, Physical Review A (2022)], including those studying quantum annealing [Das & Chakrabarti, Reviews of Modern Physics (2008);  Barends et al. Nature (2016);  Mbeng, Arceci & Santoro, Physics Review B (2019); Hatomura & Mori,  Physical Review E (2018); de Luis, Garcia-Saez & Estarellas, arXiv (2022); Bastidas et al.,  Physical Review B (2022)], discrete time crystals [Sacha & Zakrzewski, Reports on Progress in Physics (2018);  Else et al., Annual Reviews of  Condensed Matter Physics (2020);  Estarellas et al., Science Advance (2020);  Sakurai et al. Physical Review Letters (2021)], and space-time dual quantum circuits [Akila et al., Jornal of Physics A (2016);  Piroli et al. Physical Review (2020);  Bertini, Kos, & Prosen, Physical Review (2018);  Lu & Grover, PRX Quantum (2021);  Fisher et al. Annual Reviews of Condensed Matter Physics (2023)], rely on the fact that the dynamics depend on iterated processes.".  

♦ Tan et al.  (National University of Singapore, Singapore;  Technical University of Crete, Greece;  ...) write in the Introduction of their  Physical Review A (January, 2024), summarizing the present scenario of quantum optimization,  "Quantum algorithm to find the ground state include Quantum Annealing [Rajak et al., Philosophical Transactions of the Royal Society A (2023); Santoro & Tosatti, Journal of Physics A: Math. Gen. (2006); Das & Chakrabarti, Reviews of Modern Physics (2008)], variational problem-specific algorithms such as the Quantum Approximate Optimization Algorithm and its generalizations [Farhi et al., arXiv:1411.4028 (2014); Hadfield et al., Algorithms (2019)], Variational Quantum Eigensolvers [Peruzzo et al. , Nature Communications (2014); McClean et al.,  New Journal of Physics (2016); Shaydulin et al., Computer (2019)] and Quantum Assisted methods [Bharti et al., Reviews of Modern Physics (2022);  Kyriienko,  npj Quantum Information  (2020); Bharti & Haug,  Physical Review A (2021)]. "       

♦ Giordani, Suprano & Sciarrino (Dipartimento di Fisica, Sapienza Università, Roma)  write in the Introduction of  their The Second Quantum Revolution:  Quantum Computer  & Encryption (January, 2024)  "Analog quantum computation is advantageous when we want to create simulation algorithms of a Hamiltonian for which  it is difficult to identify eigenvalues ​​and eigenvectors, or, algorithms of optimization in which the solution is made to coincide with the problem at a  fundamental level of the Hamiltonian of the quantum processor [Das & Chakrabarti, Reviews  of Modern Physics  (2008)]."  (Google Translate). 

♦ Bastidas, ... Chuang et al.  (Dept. Phys., Harvard University, Massachusetts; Dept. Phys., MIT, Massachusetts; ...) write in the Introduction of  their Physical Review B (January, 2024)  "... most explorations into the nonequilibrium behavior of condensed matter systems [Polkovnikov et al., Reviews of Modern Physics (2011); Hatomura, Physical Review A (2022)], including those studying quantum annealing [Das & Chakrabarti, Reviews  of Modern Physics  (2008); Barends, et al., Nature (2016); Mbeng,  Arceci & Santoro, Physical Review B (2019); Hatomura & Mori, Physical Review  E (2018);  de Luis, Garcia-Saez & M. P. Estarellas, arXiv:2206.07646 (2022); Bastidas et al., Physical Review B (2022); Hatomura, New Journal of Physics (2020)], discrete time crystals [...], and space-time dual quantum circuits [...], rely on the fact that the dynamics depend on iterated processes." ... "In this paper we apply Quantum Signal Processing-inspired techniques to the one-dimensional quantum transverse-field Ising mode, a condensed matter system which is of general theoretical interest from quantum annealing [Das & Chakrabarti, Reviews  of Modern Physics  (2008)] to space-time dual circuits  [...], and one that is routinely realized experimentally indiverse noisy intermediate scale quantum platforms [...]."

♦Date et al. (Oak Ridge National Laboratory, Oak Ridge), in  their  Adiabatic Quantum Support Vector Machines (arXiv, January 2024) write  "Although the theoretical time complexity of quantum annealing used to obtain an exact solution is exponential (O(e^√d)) [Mukherjee & Chakrabarti, European Physical Journal: Special Topics (2015)], a more realistic estimate of the running time can be made by using measures such as ST99 and ST99(OPT) [Wang & Jonckheere, Quantum Information Processing (2019)], which give the expected number of iterations to reach a certain level of optimality with 99% certainty."

♦ Ren,  König & Tsvelik (Brookhaven National Laboratory, New York;  Max-Planck Inst.  for Solid State Res., Stuttgart)  write in their Topological quantum computation on a chiral Kondo chain (Physical Review B, February 2024)  "Currently, there are four main different approaches to the quantum computing protocols: the quantum circuit model [Nielsen & Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press (2010)], the measurement-based quantum computation [Raussendorf  & Briegel, Physical Review Letters (2001); Raussendorf, Browne & Briegel, Physical Review A (2003)], the adiabatic quantum computation [Farhi et al., arXiv:quant-ph/0001106 (2000);  Das & Chakrabarti, Reviews of Modern Physics (2008)], and the topological quantum computation [Kitaev, Annals of Physics (2003);  Nayak et al., Reviews of Modern Physics (2008); Pachos, Introduction to Topological Quantum Computation, Cambridge University Press (2012); Lahtinen & Pachos, SciPost Physics (2017)].".

♦ Garcia-de-Andoin et al.  (University of the Basque Country, Spain;  Universidad de Sevilla, Spain; Universidad de Granada, Spain; Basque Foundation for Science, Spain; ... ) begin the Introduction of their Digital-Analog Quantum Computation with Arbitrary Two- Body Hamiltonians (Physical Review Research (March, 2024)) with the sentences "When quantum computing was originally proposed [Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, Journal of Statistical Physics (1980); Feynman, Simulating physics with computers, International Journal of Theoretical Physics (1982)], it was envisioned as a way of simulating the dynamics of a quantum system employing another controllable system. This set the foundations of what we now call analog quantum computing [Das & Chakrabarti, Colloquium: Quantum annealing and analog quantum computation, Reviews  of Modern Physics  (2008)]. A different approach was introduced when Deutsch proposed the concept of a quantum gate [Deutsch, Barenco & Ekert, Universality in quantum computation,  Proceedings of the Royal Society A (1995)], which finally led to the digital quantum computing paradigm."

♦ Coffrin & Vuffray (Los Alamos National Laboratory, Los Alamos, NM, USA) start their Introduction to 'Quantum Annealing'  in  Encyclopedia of Optimization (March  2024) with the sentence  "The quantum annealing algorithm was proposed in the 1990s with the aim of providing a fast heuristic for solving unconstrained combinatorial optimization problems [Kadowaki & Nishimori, Physical Review E (1998); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Finnila et al., Chemical Physics Letters (1994); Farhi et al., Science (2001); Santoro et al., Science (2002)]. Quantum annealing is an analog quantum algorithm that combines the mathematical properties of quantum systems and continuous time evolution to minimize a discrete function."

♦ Zhang, Boothby & Kamenev (Univ. Minnesota, Minneapolis;  D-Wave Systems Inc., British Columbia) start the  Introduction of their Cyclic Quantum Annealing: Searching for Deep Low-Energy States in 5000-Qubit Spin Glass (arXiv, March, 2024) with the sentences:  "The concept of a quantum computer, as originally envisioned by Feynman [Feynman, International Journal of Theoretical Physics (1982)], is a system comprising a large number of spins. ...  such problems can be formulated in terms of finding low-energy states of spin systems [Barahona, Journal of Physics A: Math. Gen. (1982);  Farhi et al., Science (2001);  Battaglia, Santoro &Tosatti, Physical Review E (2005);  Lucas,  Frontiers in Physics (2014)]. Quantum annealing uses quantum fluctuations to navigate the system between local minima towards its low energy states. It has been designed, developed and validated as an effective method for  an approximate solution of these optimization tasks [Brooke et al., Science (1999);  Frarhi et al., Science (2001);  Kirkpatrick, Gelatt & Vecchi, Science (1983);  Finnila et al., Chemical Physics Letters (1994); Kadowaki & Nishimori, Physical Review E (1998); Santoro et al., Science (2002); Das & Chakrabarti, Reviews of Modern Physics (2008); Morita & Nishimori, Journal of Mathematical Physics  (2008); Young, Knysh, Smelyanskiy, Physical Review Letters (2010); Albash & Lidar, Reviews of Modern Physics (2018); Ohkuwa, Nishimori & Lidar, Physical Review A (2018); Yamashiro et al., Physical Review A (2019); Hauke et al., Reports on Progress in Physics (2020); Passarelli et al., Physical Review A (2020); Rajak et al., Philosophical Transactions of the Royal Society A: Math, Phys & Eng Sciences (2023)]. Ideally, the ground state is attainable if the adiabatic condition is strictly met [Das & Chakrabarti, Reviews of Modern Physics (2008);  Morita & Nishimori, Journal of Mathematical Physics  (2008) ;  Albash & Lidar, Reviews of Modern Physics (2018); Santoro  & Tosatti, Journal of Physics A: Math & Gen. (2006)]. However, the spin-glass phase [Harris et al., Science (2018); Santoro et al., Science (2002); Edwards & Anderson, Journal of Physics F: Metal Physics (1975);   Binder & Young,  Reviews of Modern Physics (1986); Crisanti et al., Physical Review B (2003); Cavagna, Giardina & Parisi, Physical Review Letters (2004);  Mukherjee, Rajak & Chakrabarti, Physical Review E (2018)] presents significant challenges, characterized by a vast number of local minima and exponentially small energy gaps, which require exponential time to satisfy adiabaticity. Any deviations from adiabaticity lead to a cascade of Landau-Zener transitions to higher energy states, making deep low-energy states improbable.".  

♦ Tikhanovskaya,  Sachdev  & Samajdar  (Harvard University, Cambridge; Princeton University, Princeton)  start the Introduction of  their PRX Quantum  (April, 2024) with the sentences "Modern advances in the development and control of programmable quantum simulators [Ebadi, et al., Science (2022); King et al., Nature (2023); ...] have led to remarkable implementations of the idea of solving classical optimization problems by quantum tunnelling [Brooke et al., Science (1999); Farhi et al., Science (2001)]. ... This model has been much studied in the quantum spin-glass literature [Yamamoto &  Ishii, Jpurnal of Physics C (1987); Kopeć, Usadel & Büttner, Physical Review B (1989); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989);  Büttner & Usadel,   Physical Review B  (1990) ; Miller & Huse, Physical Review Lettets (1993);  Ye,  Sachdev & Read, Phydsical Review Letters (1993); Read, Sachdev & Ye, Physical Review B (1995); Rozenberg  & Grempel, Physical Review Letters (1998); Kennett, Chamon & Ye, Physical Review B (2001);  Arrachea & Rozenberg, Physical Review Letters (2001);  Takahashi, Physical Review B (2007); Andreanov & Müller, Physical Review Letters (2012); Mukherjee, Rajak & Chakrabarti, Physical Review E (2015); Mukherjee, Rajak & Chakrabarti, Physical Review E (2018); Young, Physical Review E (2017); Leschke et al., Physical Review Letters (2021); Kiss, Zaránd & Lovas, Physical Review B (2024)], but only a few results have been obtained for the model with a nonzero field [...], which is an essential ingredient in the optimization toolbox of Rydberg quantum simulators.".

♦ Shingu et al.  (Dept. Phys., Tokyo Univ. of Science, Tokyo; Quantum-AI Tech., National Inst. of Adv. Industr. Sc. & Tech.,  Ibaraki)  start the Introduction of  their Quantum annealing with error mitigation (Physical Review A, April, 2024) with the sentences "Quantum annealing (QA) [Kadowaki & Nishimori, Physical Review E (1998); Farhi et al.  arXiv (2000);  Farhi et al., Science (2001); Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Finnila et al., Chemical Physics Letters (1994)] is a promising approach for obtaining the ground state of a problem Hamiltonian HP. Initially, the system is prepared as the ground state of a driver Hamiltonian HD. In QA, we employ a time-dependent total Hamiltonian that changes from HD to HP, and we let the state evolve by such a Hamiltonian. As long as the adiabatic condition is satisfied, we can obtain the ground state of HP  after the dynamics without noise [Ehrenfest, Adiabatische Invarianten und Quantentheorie, Annalen der Physik (1916); Kato, On the adiabatic theorem of quantum mechanics, Journal of the Physical Society of Japan  (1950), ...]." [Also discusses Das & Chakrabarti, Reviews  of Modern Physics  (2008) in the section on QA].

♦Zhao et al. (Wuhan National High Magnetic Field Center & School of Physics, Huazhong Univ. of Sc. & Tech., Wuhan; ...), write in their  Quantum annealing of a frustrated magnet, Nature Communications (April 2024) "Quantum annealing (QA), which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet α-CoV2O6, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field.", in the Abstract and write in the Introduction "[the only earlier] reported example of an Ising spin glass, LiHoxY1−xF4, that exhibits many-body QA phenomena [Brooke et al.,  Science (1999);  Brooke, Rosenbaum & Aeppli, Nature (2001);   Das & Chakrabarti, Reviews  of Modern Physics  (2008)] ... [where the] disorder of Ho and Y introduces interaction randomness, making it challenging to create a precise microscopic model of this system.".

♦ Barone (Univ. Padua) in the thesis (Supervisors from Univ. Innsbruck & Univ. Padua) entitled  Floquet counterdiabatic protocols for Quantum Annealing on Parity architecture (April 2024, available onlin, write (in Sec. 2.3 on Quantum Annealing) "The concept of random noise can be formalized within statistical mechanics as a thermal fluctuation, with the temperature T playing the role of a noise factor [Das & Chakrabarti, Reviews of Modern Pysics (2008)]. Higher temperatures produce strong fluctuations. Simulated Annealing is a method for solving optimization problems that takes advantage of thermal fluctuations in a simulated environment [Kirkpatrick, Gelatt, & Vecchi ] ... Optimization algorithms that exploit spin-glass dynamics show a coarse(quantum) energy landscape, with many local minima. Introducing fluctuations is a reasonable mitigation method, even though there might be further complications. Indeed, in a glassy landscape, local minima might be surrounded by high energy barriers, making the optimization based on thermal noise less effective. Furthermore, the energetic barriers may be proportional to the system size and diverge in the thermodynamic limit, especially if the underlying interactions. Luckily, the quantum nature of the system allows us to take advantage of another type of statistical fluctuations, which are due to quantum tunneling [Das & Chakrabarti, Reviews of Modern Physics (2008); Ray, Chakrabarti, Chakrabarti, Physical Review B (1989)]. Fluctuations due to quantum tunneling behave differently from (classical) thermal fluctuations. In the latter, the system has to gain sufficient energy in order to cross an energy barrier. Instead, in quantum tunneling, the crossing is under stood in terms of probability and can occur even if the system does not match the energy requirement, provided the barrier is thin enough."

♦ Alsing, Cafaro & Mancini (Univ.  at Albany-SUNY, NY; ... ; INFN, Sezione di Perugia, Perugia) start their (invited) paper Feynman’s 'Simulating Physics with Computers' (International Journal of Theoretical Physics, May 2024) with the sentences "Feynman delivered his seminal lecture 'Simulating physics with computers' at the Physics of Computation Conference at the MITEndicott House in May of 1981. The content of his lecture was later published by the International Journal of Theoretical Physics in 1982 [Feynman, International Journal of Theoretical Physics (1982)]. Nowadays, Feynman’s 1982 paper is properly regarded as one of the most influential pieces of work that helped laying out the foundations of quantum computing as a research discipline in its own right. ... Returning to the concept of quantum simulations, one can also use as a quantum simulator an alternative device built specifically for the simulation, for instance a quantum annealer [Das & Chakrabarti, Reviews of Modern Physics (2008)]. Actually, it is possible to identify three types of simulation [Gorgescu, Ashhab & Nori, Reviews of Modern Physics (2014)] : i) digital simulation; ii) analog quantum simulation (including, for instance, quantum annealing [Das & Chakrabarti, Reviews of Modern Physics (2008)]); iii) quantum-information inspired algorithms for the classical simulation of quantum systems.". 

♦ Mattesi  et al. (Dept. Math.  Sciences, Politecnico di Torino, Torino; ...)  write in the section on Quantum Annealing of their Diversifying Investments and Maximizing Sharpe Ratio (quantum  reports, May 2024) "Quantum annealing is a heuristic optimization procedure proposed in [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989)] ... For further details, one can refer to [Glover, Kochenberger & Du, arXiv:1811.11538 (2018)] for the definition of effective QUBO formulations and to [Rajak et al., Philosophical Transactions of the Royal Society A (2023)] for quantum annealing."

♦Huang & Ju (Shanghai Jiao Tong Univ., Shanghai) write in the section on 'Quantum Annealing in a Quantum Virtual Machine' of their Journal of Applied Physics (May 2024) "Quantum annealing (QA) is an optimization algorithm assisted by Ising machines to search for the global minimum of a given problem over a given set of candidate solutions (candidate states) [Ray, Chakrabarti & Chakrabarti, Physical Review B (1989); Kadowaki & Nishimori, Physical Review E (1998)],  which are implemented with superconducting qubits, ASICs, GPUs, and so on [Mao et al., Digital Discovery (2023)]. QA a has been successfully applied to the design of inorganic and organic materials [Mao et al., Digital Discovery (2023); Wilson et al, Applied Physics Review (2021)]. Ising machine was developed specifically for solving quadratic unconstrained binary optimization (QUBO), which is adapted to the binary sequence encoding of polymers.". [In the section on 'Polymer Modelling', the authors discuss on the self-avoiding walk models with neigbour-bridging links for polymer chains by Fisher, Journal of Chemical Physics (1966) and Chowdhury & Chakrabarti, Journal of Physics A: Math. & Gen. (1985)]

♦ Volpe et al. (Dept. Electronics & Telecommun., Dept. Engineering,  Politecnico di Torino, Torino; ...)  write in the section on Theoretical Foundations of their ACM Transactions on Quantum Computing (June, 2024) "Quantum annealers [Chakrabarti et al., Philosophical Transactions of the Royal Society A (2023); Johnson et al., Nature (2011); Kadowaki & Nishimori, Physical Review E (1998); Rajak et al., Philosophical Transactions of the Royal Society A (2023)]  are special-purpose quantum computers that allow the minimization of a problem’s cost function, formulated in either Ising or QUBO representation, through an adiabatic evolution of their quantum system. Nowadays, they are the best-performing quantum solvers, in terms of complexity of processable optimization problems.".    

♦ Aonishi et al. (University of Tokyo, Chiba; Tokyo Institute of Technology, Yokohama; Hiroshima City University, Hirosima; ...)  write in the Introduction of their Highly Versatile FPGA-Implemented Cyber Coherent Ising Machine (arXiv, June 2024) "Several quantum Ising machines have been proposed. This includes D-Wave systems [Johnson et al, Nature (2011); KIng et al., Nature (2018)], which utilize superconducting quantum interferometers [Kadowaki & Nishimori, Physical Review E (1998); Brooke et al., Science (1999); Das & Chakrabarti, Reviews of Modern Physics (2008)]  to execute quantum annealing for adiabatic quantum computation [Farhi et al., Science (2001); Albash & Lidar, Reviews of Modern Physics (2018)]. " 

♦ Volpe et al. (Dept. Electronics & Telecommun., Dept. Engineering,  Politecnico di Torino, Torino; Chair for Design Automation,Technical University of Munich, Munich; ...)  write in the section on SOLVING OPTIMIZATION PROBLEMS WITH QUANTUM COMPUTERS of their Towards an Automatic Framework for Solving Optimization Problems with Quantum Computers (TUM Report, June 2024) "In order to exploit the quantum computing paradigm for optimization problems, there are two possibilities: employing a Quantum Annealer — a special-purpose quantum computer theorized in 1998 [Kadowaki & Nishimori, Physical Review E (1998);  Chakrabarti et al., Philosophical Transactions of the Royal Society A (2023); Rajak et al., Philosophical Transactions of the Royal Society A (2023);  Johnson et al., Nature (2011)], using the natural properties of a quantum system evolution for obtaining the ground state—or executing algorithms entirely or partially on a general-purpose quantum computer compliant with the quantum circuit model [Nielsen & Chuang, Quantum computation and quantum information, Cambridge Univ. Press , 10th Ed. (2010)],"

♦ Endo et al. (National Institute of Advanced Industrial Science and Technology, Tsukuba; Keio University, Yokohama & Tokyo;   Waseda University, Tokyo; ...)  start the Introduction of  their PLOS ONE (June, 2024)  with the sentences "Next-generation accelerators including quantum computers are steadily developing. In particular, quantum annealing machines [Kadowaki & Nishimori, Physical Review E (1998); Johnson et al., Nature (2011); Tanaka, Tamura & Chakrabarti, Quantum Spin Glasses, Annealing and Computation,  Cambridge Univ. Press (2017); Denchev et al., Physical Review X (2016);  Das & Chakrabarti, Reviews of Modern Physics (2008); Santoro & Tosatti, Journal of Physics A: Math & Gen (2006)] can search for the minimum value of the objective function at high speed [Rønnow et al., Science  (2014)]. "

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