Automatic design of Hamiltonians. (arXiv:1907.05898v1 [quant-ph])

We formulate an optimization problem of finding optimal Hamiltonians by
analogy to the variational principle. Given a variational ansatz for a
Hamiltonian we construct a loss function as a weighted sum of relevant
Hamiltonian properties specifying thereby the search query. Using fractional
quantum Hall effect as a test system we illustrate how the framework can be
used to determine a generating Hamiltonian of a finite-size model wavefunction
(Moore-Read Pfaffian and Read-Rezayi states) or to find optimal parameters for
an experiment. We also discuss how the search for approximate generating
Hamiltonians may be used to find simpler and more realistic models implementing
the given exotic phase of matter by experimentally accessible interaction
terms.

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