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The coin example is incorrect (that is, different from QM) if you consider correlations of measurements of entangled qubits in different bases.
If you want a more advanced attempt of building a deterministic theory underlying QM, have a look at Gerard 't Hooft book The Cellular Automaton Interpretation of Quantum Mechanics which is free now.
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Einstein, Podolsky and Rosen's (local) Hidden Variable theory is the most famous deterministic attempt to explain Quantum Mechanics. You can take a look at the wiki on the explanation: https://en.wikipedia.org/wiki/Hidden-variable_theory. As proved later on by Bell, this theory was not "possible" given the theory could not account for experimental ...
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Qiskit Aqua includes both algorithms:
https://qiskit.org/documentation/apidoc/qiskit.aqua.algorithms.html
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I would start from this excellent intro course by Thomas Vidick and Stephanie Wehner, available in Edx. Then take a look at some classic papers:
The one that started it all: https://core.ac.uk/reader/82447194.
The one that brought a whole new approach: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67.661
The one that simplified it somewhat: ...
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Yes, there are. I just wrote a paper about it, actually.
You need to define carefully what you mean by obtaining a Bell violation or ruling out local hidden variables. You can't demand to have a result which is impossible to explain with local hidden variables: the local bound of a Bell inequality is inherently probabilistic, so it is possible to obtain any ...
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We can find a number of good articles on Hamiltonians in Adiabatic Quantum Computing. Please let me share a few prominent articles here.
Hamiltonian engineering for adiabatic quantum computation: Kazutaka Takahashi
Adiabatic Quantum Computation with a 1D projector Hamiltonian
Non-diagonal problem Hamiltonian for adiabatic quantum computation
Realizable ...
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