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arXiv · 1002.2219

Adiabatic Markovian Dynamics

Ognyan Oreshkov·John Calsamiglia
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Abstract

We propose a theory of adiabaticity in quantum Markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the underlying Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As an application of our theory, we propose a framework for decoherence-assisted computation in noiseless codes under general Markovian noise. We also formulate a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by non-dissipative means.

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Ognyan Oreshkov, John Calsamiglia. 2010-07-30. Adiabatic Markovian Dynamics. https://doi.org/10.1103/physrevlett.105.050503

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