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Physics Letters A

Geometry of quantal adiabatic evolution for systems with a degenerate Hamiltonian

Jianming Li, Zhaoyan Wu

Published Sep 1, 1992• 3 citations
Publisher
DOI
10.1016/0375-9601(92)90514-m

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Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counterdiabatic Hamiltonian to stifle nonadiabatic transitions. Here this shortcut to adiabaticity is cast in terms of a generator of adiabatic transport. This yields a classical analog of transitionless driving, and provides a strategy for constructing quantal counterdiabatic Hamiltonians. As an application of this framework, exact classical and quantal counterdiabatic terms are obtained for a particle in a box and for even-power-law potentials in one degree of freedom.
An ANN(artificial neural network)-inspired quantum adiabatic evolution algorithm, which is a new quantum computation algorithm based on both the ANNlike method and the adiabatic Hamiltonian evolution, has been proposed for solving a combinatorial optimization problem. However, it has been known that the adiabatic evolution algorithm can not be applied to a quantum system with degenerated states during the evolution of a Hamiltonian. In order to remove this limitation, we propose an improved ANN-inspired algorithm with energy dissipation and discuss how to use this algorithm for solving an optimization problem.