Adiabatic approximation for weakly open systems
Open accessAbstract
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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Markovian dynamics requires either the singular coupling limit (high temperature) or the weak coupling limit (weak system-bath interaction).
“Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction).”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [37]
The Davies derivation can be generalized to allow for slowly varying system Hamiltonians, whenever the time scale of variation of H_C(t) is much longer than the inverse of the typical Bohr frequency of H_S.
“Davies did not consider time-dependent system Hamiltonians in [43], but it is possible to generalize his derivation to allow for slowly varying system Hamiltonians [37, 44, 45]. That is, whenever the time scale of the variation of H C ( t ) is much longer than the inverse of the typical Bohr frequency (of H S ), it is possible to add H C ( t ) to the system Hamiltonian in Eq. (23), necessitating a”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [37]
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- Authors
- Thunström, P., Åberg, J., & Sjöqvist, E.
- Affiliations
- Uppsala University (SE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2005-08-18
- Volume
- 72
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2289110952
- Cited by
- 49
- References
- 28
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 3 · 2021: 3 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 2 · 2016: 5 · 2015: 1 · 2014: 1 · 2013: 3 · 2012: 2
- FWCI
- 3.88
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- adiabatic approximation, open quantum systems, completely positive maps, master equation, holonomic quantum computation, non-Abelian holonomy, Hadamard gate, decoherence
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