A note on the switching adiabatic theorem

DOI10.1063/1.4748968zbMath1283.81034arXiv1204.2318OpenAlexW3102148282WikidataQ58004532 ScholiaQ58004532MaRDI QIDQ2872285

George A. Hagedorn, Alexander Elgart

Publication date: 14 January 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2318

zbMATH Keywords

algorithmic complexityadiabatic quantum computingGevrey class Hamiltonianminimum energy gapNenciu expansion

Mathematics Subject Classification ID

Quantum computation (81P68) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to ordinary differential equations (34E05) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum algorithms and complexity in the theory of computing (68Q12)

Related Items (3)

Least-squares solutions to polynomial systems of equations with quantum annealing ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2

Cites Work

• Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
• Adiabatic invariance to all orders
• Exponentially small adiabatic invariant for the Schrödinger equation
• Adiabatic theorem without a gap condition
• Erratum: Adiabatic theorems and applications to the quantum Hall effect
• Linear adiabatic theory. Exponential estimates
• On the efficiency of Hamiltonian-based quantum computation for low-rank matrices
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• A Note on Exponential Estimates in Adiabatic Theory
• Bounds for the adiabatic approximation with applications to quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• On the adiabatic theorem of quantum mechanics
• Superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum
• Precise exponential estimates in adiabatic theory
• Adiabatic charge transport and the Kubo formula for Landau-type Hamiltonians
• EXPONENTIAL APPROACH TO THE ADIABATIC LIMIT AND THE LANDAU-ZENER FORMULA
• Elementary exponential error estimates for the adiabatic approximation.

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