, Volume 17, Issue 4, pp 335–371 | Cite as

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

  • Fred GloverEmail author
  • Gary Kochenberger
  • Yu Du
Invited Survey


Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the first of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications, with an emphasis on supplementing models with numerical illustrations. In Part 1 (the present paper) we focus on the Quadratic Unconstrained Binary Optimization model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems.


Quadratic Unconstrained Binary Optimization (QUBO) Quantum computing Quantum Bridge Analytics Combinatorial optimization 

Mathematics Subject Classification

90C27 81P68 11E16 



This tutorial was influenced by our collaborations on many papers over recent years with several colleagues to whom we owe a major debt of gratitude. These co-workers, listed in alphabetical order, are: Bahram Alidaee, Dick Barr, Andy Badgett, Rajesh Chawla, Yu Du, Jin-Kao Hao, Mark Lewis, Karen Lewis, Zhipeng Lu, Abraham Punnen, Cesar Rego, Yang Wang, Haibo Wang and Qinghua Wu. Other collaborators whose work has inspired us are too numerous to mention. Their names may be found listed as our coauthors on our home pages.

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ECEE, College of Engineering and Applied ScienceUniversity of ColoradoBoulderUSA
  2. 2.Business SchoolUniversity of Colorado at DenverDenverUSA

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