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arXiv · 1406.7138

Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm

Sangchul Oh·Sabre Kais
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Abstract

We study quantum dynamics of Grover's adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolutions are visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for short running time to inverse-square decay for long running time. The size dependence of the critical running time is expressed in terms of Lambert $W$ function. The transitionless driving Hamiltonian is obtained to make a quantum state follow the adiabatic path. We demonstrate that a constant Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with running time. This may open up a new way of reducing errors in adiabatic quantum computation.

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Sangchul Oh, Sabre Kais. 2014-06-27. Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm. https://doi.org/10.1063/1.4903451

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