Geometric Speed Limit of Accessible Many-Body State Preparation

  title={Geometric Speed Limit of Accessible Many-Body State Preparation},
  author={Marin Bukov and Dries Sels and Anatoli Polkovnikov},
  journal={Physical Review X},
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic… 

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