Driving at the quantum speed limit: optimal control of a two-level system
Open accessAbstract
A remarkably simple result is derived for the minimal time Tmin required to drive a general initial state to a final target state by a Landau-Zener-type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is also derived. A surprise arises for some states when the interaction strength is bounded by a constant c. Then, for large c, the optimal driving is of type bang-off-bang and for increasing c one recovers the unconstrained result. However, for smaller c the optimal driving can suddenly switch to bang-bang type. We discuss the notion of quantum speed limit time.
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If the initial state is the ground state at Γ(0) = -γ and the final target is the excited state at Γ(τ) = γ, then the minimal time is one over the square root of γ squared plus ω squared, which is less than pi over twice ω, the quantum speed limit time.
“if the initial state, |ψ 0 , is the ground state at Γ(0) = -γ while the final target state, |ψ T , is the excited state at Γ(τ ) = γ it can be shown that τ min = 1 γ 2 + ω 2 < π 2ω = τ QSL .(64)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [116]
Hegerfeldt showed that the optimal control problem for a two-level system is analytically treatable for arbitrary initial and final states.
“Hegerfeldt showed that the optimal control problem for a two level system is analytically treatable for arbitrary initial and final states.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [116]
The analytical formulas of the fidelity F(ρ0,ρτ) and the affinity A(ρ0,ρτ) for any pair of one-qubit states are given by Eqs. (A12) and (A13).
“where the analytical formulas of the fidelity Fðρ 0 ; ρ τ Þ and the affinity Aðρ 0 ; ρ τ Þ for any pair of one-qubit states ρ 0 and ρ τ are the following [29,73,74]:”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [29]
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- Authors
- Hegerfeldt, G. C.
- Affiliations
- University of Göttingen (DE)
- Corresponding author
- Hegerfeldt, Gerhard C.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2013-12-27
- Volume
- 111
- Issue
- 26
- Pages
- 260501-260501
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1992685673
- Cited by
- 232
- References
- 21
- Citations by year
- 2026: 4 · 2025: 17 · 2024: 19 · 2023: 25 · 2022: 17 · 2021: 20 · 2020: 23 · 2019: 15 · 2018: 15 · 2017: 19 · 2016: 20 · 2015: 28 · 2014: 10
- FWCI
- 21.38
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- GRO (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum speed limit, optimal control, two-level system, Landau-Zener model, minimal time, bang-bang control, state-to-state transitions
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