Still waiting · [Oct 10, 01:48 PM]
So the Ph.D project is finished but I still have to wait to jump to the next: a postdoc.
Since things are still in the air, I thought I would start thinking more about adiabatic evolution. One of the things that bugs me about most of the bounds on the precision of a quantum adiabatic evolution are based on estimates on how fast compared to the spectral gap you can vary your Hamiltonian and still get the desired evolution from one eigenstate to another. I am thinking that obviously, if the time-varying Hamiltonian commutes with itself at all times (or during sufficiently long periods) such estimates are meaningless. So why aren’t we basing the estimates on some sort of commutator integral instead?
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