Linearity and Quantum Adiabatic Theorem

2007/01/19 by Zhaohui Wei, Mingsheng Ying, Wei, Zhaohui +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.quant-ph/0701135

openalex publication_date 2007/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the application of the linearity and the adiabatic approximation simultaneously. Besides, based on this observation we point out the mistake in the traditional proof for the adiabatic theorem. This mistake is the root of the troubles that the adiabatic theorem has met. We also show that a similar mistake remains in some recent modifications of the traditional adiabatic theorem attempting to eliminate the troubles.

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