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arXiv · 0801.3872

The adiabatic theorem in the presence of noise

Michael J. O'Hara·Dianne P. O'Leary
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Abstract

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results.

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Michael J. O'Hara, Dianne P. O'Leary. 2008-01-25. The adiabatic theorem in the presence of noise. https://doi.org/10.1103/physreva.77.042319

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