A note on the switching adiabatic theorem

Abstract

We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^{\alpha }$ as a function of time, and we show that the error in adiabatic approximation remains small for running times of order $g^{-2}|\ln g{|}^{6\alpha }$. Here $g$ denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.

20 pages, no figures, to appear in JMP

References in corpus (3)

• Bounds for the adiabatic approximation with applications to quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• On the efficiency of Hamiltonian-based quantum computation for low-rank matrices

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