Having previously studied general aspects of QUBO models, we now study application specific examples and how to derive or set them up. Our application examples will consider problems in areas like combinatorial optimization, constraint satisfaction, data mining, and machine learning and are supposed to illustrate that QUBOs provide us with a surprisingly versatile and widely applicable modeling framework. Put differently, our overall goal with this chapter is to demonstrate how to rethink familiar, seemingly unrelated problems in terms of an overarching formalism that will later allow for running Hopfield nets and quantum implementations. This will largely be an exercise in applied linear algebra since we will extensively work with matrix-vector formulations of QUBOs for which we will point out and discuss simplifying modeling assumptions whenever necessary.

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QUBO Models

  • Christian Bauckhage,
  • Rafet Sifa

摘要

Having previously studied general aspects of QUBO models, we now study application specific examples and how to derive or set them up. Our application examples will consider problems in areas like combinatorial optimization, constraint satisfaction, data mining, and machine learning and are supposed to illustrate that QUBOs provide us with a surprisingly versatile and widely applicable modeling framework. Put differently, our overall goal with this chapter is to demonstrate how to rethink familiar, seemingly unrelated problems in terms of an overarching formalism that will later allow for running Hopfield nets and quantum implementations. This will largely be an exercise in applied linear algebra since we will extensively work with matrix-vector formulations of QUBOs for which we will point out and discuss simplifying modeling assumptions whenever necessary.