Adiabatic Markovian Dynamics

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.

4+3 pages

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Cited by in corpus (34)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum Adiabatic Markovian Master Equations
• Slow dynamics and thermodynamics of open quantum systems
• Coherent oscillations inside a quantum manifold stabilized by dissipation
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Geometry and response of Lindbladians
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Holonomic quantum control with continuous variable systems
• Adiabaticity in open quantum systems
• Geometric phases in quantum information
• Accuracy vs run time in adiabatic quantum search
• The structures of state space concerning Quantum Dynamical Semigroups
• Quantum Computing in Plato's Cave
• On the stability of quantum holonomic gates
• Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization
• Quantum Zeno Dynamics from General Quantum Operations
• Geometry, robustness, and emerging unitarity in dissipation-projected dynamics
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Relaxation vs. adiabatic quantum steady state preparation: which wins?
• Eigenstate Tracking in Open Quantum Systems
• Improved Boltzmann machines with error corrected quantum annealing
• Adiabatic Decoherence-Free Subspaces and its Shortcuts
• Dynamically stabilized decoherence-free states in non-Markovian open fermionic systems
• Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• Error Suppression for Hamiltonian Quantum Computing in Markovian Environments
• Non-Abelian Phases from a Quantum Zeno Dynamics
• Universal Control Induced by Noise
• Fast quantum algorithms for traversing paths of eigenstates
• Sufficient conditions for adiabaticity in open quantum systems
• Emerging unitary evolutions in dissipatively coupled systems
• Geometric phases along quantum trajectories
• Effect of decoherence on the Berry phase of a spin-half in a rotating magnetic field
• Geometric and holonomic quantum computation