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I'm trying to understand the problem of state preparation for quantum phase estimation (QPE). Specifically how states are prepared adiabatically.

I have a couple of questions:

1). Typically when one thinks of adiabatic state preparation, annealing comes to mind. However, it is also possible to do time evolution on a gate-based quantum computer with a time-dependent Hamiltonian in order to adiabatically prepare a state. Is the latter option also considered in the context of adiabatic state preparation for QPE (the few papers I have found talk about annealing)?

2). In practice we do not expect to prepare $|\psi\rangle = |\psi_0\rangle$ but instead a superposition of states that has some non-negligible overlap with the ground state. Does this mean that we can relax the requirement of adiabaticity and instead prepare a superposition of the ground and some excited states? If so, would this help to avoid the time taken for adiabatic state preparation scaling as $\frac{1}{\Delta^2}$?

Any pointers to references are also much appreciated.

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  • $\begingroup$ I asked a related question some time ago. There was a response that mentioned some detais. I would also be interested in further details of how adiabatic state preparation works. :) quantumcomputing.stackexchange.com/questions/29508/… $\endgroup$
    – Callum
    Commented Aug 25, 2023 at 11:30
  • $\begingroup$ please see quantumcomputing.stackexchange.com/help/how-to-ask. It's better to ask a single question per post, which allows for more insightful and on-point answers. You can ask different questions on different posts $\endgroup$
    – glS
    Commented Aug 25, 2023 at 13:34

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