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Add notebook simulating Hubbard Model using Qubitization #31

@tanujkhattar

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@tanujkhattar

Simulation of Hubbard model using the newly added Select / Prepare primitives is described in section V of https://arxiv.org/abs/1805.03662.

We should write a notebooks to:

  1. Implement the select and prepare unitaries tailored for hubbard model in a notebook. This would demonstrate users how they can use existing gate primitives (like UnaryIteration, PrepareUniformSuperposition etc.) and newly added API abstractions (like GateWithRegisters primitive) to implement their own optimized constructions for different chemistry use cases.

    • Note: The select / prepare gates in the notebooks should ideally just be GateWithRegisters that defined a decompose method.
    • If any gate primitives are missing, add them to the repo before implementing the notebook.
  2. Figure out and implement utilities that would enable us to get the coefficients of the Hubbard model Hamiltonian using the indexing scheme described in the paper. @ncrubin Maybe you can look into this?

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