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My main goal is to learn Quantum annealing and quantum optimization in general. This concept is elaborated in this paper. A better example is this paper. I am particularly interested in reading material where the author describes in detail without skipping any step as to how one maps the cost function of your desired optimization problem into a Hamiltonian that can then be solved using a quantum computer.

Most papers that do this, such as the ones I just showed, either assume you already know how to do the mapping and skip the mathematical steps, or will assume you are more interested in the stuff from physics pov and hardware pov. I am interested in this problem only from the algorithmic pov. I want to read tutorial style papers written for engineers interested more in the combinatorial maths and equation manipulation stuff laid out in a detailed manner.

Could you please cite videos/books/papers? If there is prereq to learn mapping costs functions to Hamiltonians then please suggest the quickest possible route for the same?

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I would recommend the following resources. Quantum annealing is about QUBO/Ising formulations. First thing would be to get familiar with the formulations, and see examples of how do you formulate a few problems:

Then, if you have a specific problem you would like to solve, search for articles related the problem with quantum annealing. Generally, they is always a section on how to formulate as a QUBO/Ising. Finally, for quantum annealing, the best resource is the D-Wave documentation. They explain many concepts very well, in a logical order.

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If you want an applied resource teaching you the theory and how to code it, check out this paper:

Theory and Implementation of the Quantum Approximate Optimization Algorithm: A Comprehensible Introduction and Case Study Using Qiskit and IBM Quantum Computers

The first two chapters go from a quadratic constrained integer optimization problem to a Hamiltonian.

You can find the associated iPython notebooks here.

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