Adiabatic Approximation for weakly open systems

Abstract

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.

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Cited by in corpus (36)

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• Holonomic quantum control with continuous variable systems
• Adiabaticity in open quantum systems
• Geometric phases in quantum information
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Decoherence in adiabatic quantum evolution - application to Cooper pair pumping
• General Adiabatic Evolution with a Gap Condition
• On the stability of quantum holonomic gates
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• Floquet theory of Cooper pair pumping
• Non-Markovian decoherence in the adiabatic quantum search algorithm
• Effective Hamiltonian approach to adiabatic approximation in open systems
• The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
• Temperature effects on mixed state geometric phase
• Eigenstate Tracking in Open Quantum Systems
• Dynamical invariants and nonadiabatic geometric phases in open quantum systems
• Adiabatic Decoherence-Free Subspaces and its Shortcuts
• Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization
• Adiabatically steered open quantum systems: Master equation and optimal phase
• A view on the open STIRAP problem
• The adiabatic theorem in the presence of noise
• Sufficient conditions for adiabaticity in open quantum systems
• Quantum adiabatic brachistochrone for open systems
• Born-Oppenheimer approximation in open systems
• Geometric phases along quantum trajectories
• Grover Speedup from Many Forms of the Zeno Effect
• Lindbladians with multiple steady states: theory and applications
• Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach
• Noise Effects on the Wilczek-Zee Geometric Phase
• Geometric and holonomic quantum computation
• Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle