The adiabatic analogue of the Margolus–Levitin theorem
Abstract
In this letter we derive the minimum time needed for any state of a given quantum system to evolve adiabatically into a distinct (orthogonal) state. This problem is relevant to deriving physical limits in quantum computation and quantum information processing. Our result represents an adiabatic analogue to the Margolus–Levitin theorem (Margolus and Levitin 1998 Physica D 120 , 188).
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Recent results on fault tolerance in non-Markovian settings make a crucial assumption about the smallness of the norm of the system-bath interaction Hamiltonian, which severely restricts the class of physical reservoirs.
“recent results on fault tolerance in non-Markovian settings [19, 20, 21, 22], while representing a significant step forward, make a crucial assumption about the smallness of the norm of the system-bath interaction Hamiltonian, which severely restricts the class of physical reservoirs.”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [19]
In the extension of FT-QEC theory to a non-Markovian setting, the crucial role of fresh and nearly pure ancillas is carried over directly and without change from Markovian FT-QEC theory.
“An important ingredient carried over directly and without change from Markovian FT-QEC theory, is the crucial role of the fresh and nearly pure ancillas [19, 20, 21].”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [19]
The assumption of a small norm of the system-bath interaction Hamiltonian is not satisfied for some standard models of open systems.
“the important assumption of a small norm of the system-bath interaction Hamiltonian (e.g., Eq. (58) in Ref. [20]) is not satisfied for some standard models of open systems.”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [19]
Cites
The maximum speed of dynamical evolution
Margolus, N., & Levitin, L. B. (1998) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00054-2 · Cited by 887 · see citing works
Quantum search by local adiabatic evolution
Roland, J., & Cerf, N. J. (2002) · Physical Review A · doi:10.1103/physreva.65.042308 · Cited by 629 · see citing works
The maximum speed of dynamical evolution
Margolus, N., & Levitin, L. B. (1998) · Cited by 475 · see citing works
How Powerful is Adiabatic Quantum ComputationPreprint
van Dam, W., Mosca, M., & Vazirani, U. V. (2001) · Cited by 203 · see citing works
How powerful is adiabatic quantum computation?
van Dam, W., Mosca, M., & Vazirani, U. (2001) · Proceedings 42nd IEEE Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2001.959902 · Cited by 175 · see citing works
Joachain, C. J., & Bransden, B. H. (2000) · Cited by 149 · see citing works
Power of Entanglement in Quantum Communication
Lloyd, S. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.167902 · Cited by 34 · see citing works
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Alicki, R., Lidar, D. A., & Zanardi, P. (2006) · Physical Review A · doi:10.1103/physreva.73.052311 · Cited by 132 · see citing works
APPLICATIONS OF FINSLER GEOMETRY TO SPEED LIMITS TO QUANTUM INFORMATION PROCESSING
RUSSELL, B., & STEPNEY, S. (2014) · International Journal of Foundations of Computer Science · doi:10.1142/s0129054114400073 · Cited by 15 · see citing works
- Authors
- Andrecut, M., & Ali, M. K.
- Affiliations
- University of Lethbridge (CA)
- ORCID
- Ali, M K
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2004-03-29
- Volume
- 37
- Issue
- 15
- Pages
- L157-L160
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1988077786
- Cited by
- 23
- References
- 7
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 4 · 2022: 2 · 2021: 1 · 2019: 1 · 2018: 3 · 2015: 1 · 2014: 2 · 2013: 3
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Funders
- Defence Research and Development Canada
- Natural Sciences and Engineering Research Council of Canada
- 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 evolution, minimum time, quantum state evolution, orthogonal states, quantum information processing, adiabatic quantum computation
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