Adiabatic Markovian Dynamics

TL;DR

This paper develops a theory of adiabaticity for quantum Markovian systems, linking it to noiseless subsystems and proposing applications in decoherence-assisted and holonomic quantum computation.

Contribution

It introduces a novel approach to quantum adiabaticity in open systems using noiseless subsystems, providing a physical and intuitive framework.

Findings

Defines adiabaticity via noiseless subsystems in Markovian dynamics

Proposes a framework for decoherence-assisted quantum computation

Formulates a dissipation-driven approach to holonomic quantum computation

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.