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Consistency of the Adiabatic Theorem

M. H. S. Amin
2009 Physical Review Letters  
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy.  ...  In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.  ...  The author is pleased to acknowledge fruitful discussions with D.V. Averin, A.J. Berkley, F. Brito, V. Choi, E. Farhi, J. Johansson, W.M. Kaminsky, D. Lidar, R. Raussendorf, and G. Rose.  ... 
doi:10.1103/physrevlett.102.220401 pmid:19658845 fatcat:qre3h6genzbd7jujhenda5ad5i

Consistency of the Adiabatic Theorem [article]

M.S. Sarandy, L.-A. Wu, D.A. Lidar (Center for Quantum Information and Quantum Control, University of Toronto)
2005 arXiv   pre-print
Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.  ...  We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev.  ...  Acknowledgments The research of the authors is sponsored by CNPq-Brazil (to M.S.S.), and the Sloan Foundation, PREA and NSERC (to D.A.L.).  ... 
arXiv:quant-ph/0405059v3 fatcat:zd75aq2s5zd7dentbdlm4luufa

Consistency of the Adiabatic Theorem

M. S. Sarandy, L.-A. Wu, D. A. Lidar
2004 Quantum Information Processing  
Lett. 93, 160408 (2004).) and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.  ...  We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems (K.P. Marzlin and B.C. Sanders, Phys. Rev.  ...  ACKNOWLEDGMENTS The research of the authors is sponsored by CNPq-Brazil (to M.S.S.), and the Sloan Foundation, PREA and NSERC (to D.A.L.).  ... 
doi:10.1007/s11128-004-7712-7 fatcat:r524ydgpa5dnlehb5f2ci43bz4

Consistency of the adiabatic theorem and perturbation theory [article]

Marco Frasca
2012 arXiv   pre-print
We present an analysis of the adiabatic approximation to understand when it applies, in view of the recent criticisms and studies for the validity of the adiabatic theorem.  ...  We point out that this approximation is just the leading order of a perturbation series, that holds in a regime of a perturbation going to infinity, and so the conditions for its validity can be only obtained  ...  of the adiabatic theorem.  ... 
arXiv:1107.4971v3 fatcat:3ph6nbit35bgla42pzysyhlh64

A relation between fidelity and quantum adiabatic evolution

Zhaohui Wei, Mingsheng Ying
2006 Physics Letters A  
In this paper, we discuss the accurate relation between the running time and the distance of the initial state and the final state of a kind of quantum adiabatic evolutions.  ...  We show that this relation can be generalized to the case of mixed states.  ...  This is consistent with the result of [3] . Similarly, In [8] S. Das et al. implement Deutsch's algorithm [9, 10] by an adiabatic evolution of the form discussed in Theorem 1.  ... 
doi:10.1016/j.physleta.2006.03.064 fatcat:bsrq4by62zf4daglpwhpf7c2se

Adiabatic Theorem for Discrete Time Evolution

Atushi Tanaka
2011 Journal of the Physical Society of Japan  
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.  ...  This research was supported by the Japan Ministry of Education, Culture, Sports, Science and Technology under Grant number 22540396.  ...  In the following, we will follow a "discrete analog" of the conventional proof of the adiabatic theorem. 9, 10) Our proof consists of two parts.  ... 
doi:10.1143/jpsj.80.125002 fatcat:tc5mlvdotrb2zlflhwvxhtmgjq

Experimental Study of the Validity of Quantitative Conditions in the Quantum Adiabatic Theorem

Jiangfeng Du, Lingzhi Hu, Ya Wang, Jianda Wu, Meisheng Zhao, Dieter Suter
2008 Physical Review Letters  
While this quantum adiabatic theorem (QAT) is a well-established fact, it appears to be difficult to formulate a consistent quantum adiabatic condition (QAC), which unambiguously states when the theorem  ...  The quantum adiabatic theorem plays an important role in quantum mechanics.  ...  While this quantum adiabatic theorem (QAT) is a well-established fact, it appears to be difficult to formulate a consistent quantum adiabatic condition (QAC), which unambiguously states when the theorem  ... 
doi:10.1103/physrevlett.101.060403 pmid:18764440 fatcat:gi3chyy36vdcph5fqdbxv6dfqm

Is the quantum adiabatic theorem consistent? [article]

Jiangfeng Du, Lingzhi Hu, Ya Wang, Jianda Wu, Meisheng Zhao, and Dieter Suter
2008 arXiv   pre-print
The quantum adiabatic theorem states that if a quantum system starts in an eigenstate of the Hamiltonian, and this Hamiltonian varies sufficiently slowly, the system stays in this eigenstate.  ...  We investigate experimentally the conditions that must be fulfilled for this theorem to hold.  ...  Financial support comes from National Nature Science Foundation of China, the CAS, Ministry of Education of PRC, and the National Fundamental Research Program.  ... 
arXiv:0801.0361v1 fatcat:dns6iijltjgwpnxhds6goj2yxi

Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits

Shi-Jian Gu
2009 Physical Review E  
In this work, we examine the validity of quantum adiabatic theorem in thermodynamic systems.  ...  Our result, therefore, provides a quantitative time scale of the quantum adiabatic theorem in thermodynamic systems.  ...  In this work, we examine the validity of quantum adiabatic theorem in thermodynamic systems.  ... 
doi:10.1103/physreve.79.061125 pmid:19658491 fatcat:rutyjyhw2rhfjmuq6bm2jfvkqu

Adiabatic theorem for the time-dependent wave operator

David Viennot, Georges Jolicard, John P. Killingbeck, Marie-Yvonne Perrin
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
It is first shown that the adiabatic limit of the time-dependent wave operator corresponds to a succession of instantaneous static Bloch wave operators.  ...  The application of time-dependent wave operator theory to the development of a quantum adiabatic perturbation theory is treated both theoretically and numerically, with emphasis on the description of field-matter  ...  It shows both the consistency of the wave operator theorem ͑which is satisfied with a precision less than 10 −30 when the adiabatic parameter is constant͒ and the use of a two-time formalism in the framework  ... 
doi:10.1103/physreva.71.052706 fatcat:3rvufpjoivdwfho6sbjctzxbou

Solid Soft Theorems [article]

Enrico Pajer, Sadra Jazayeri, Drian van der Woude
2019 arXiv   pre-print
Then, from the corresponding symmetries of the action of perturbations we compute the leading order related soft theorems using the operator product expansion.  ...  To this end, we first derive all cosmological adiabatic modes for solids, which display the interesting novelty of non-vanishing anisotropic stresses on large scales.  ...  P. have been supported by the Delta-ITP consortium, a program of the Netherlands Organization for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).  ... 
arXiv:1902.09020v1 fatcat:muygfdxcsrfp5nppweuizllk6i

Common Gnoseological Meaning of Gödel and Caratheodory Theorems [chapter]

Bohdan Hejna
2019 Ontology in Information Science [Working Title]  
By using physical terms of the adiabatic changes the Caratheodory theorems express the properties of the Peano Arithmetic inferential process (and even properties of any deductive and recursively axiomatic  ...  Law of Thermodynamics are physically analogous with the real sense of the Gödel's wording of his I. and II. incompleteness theorems.  ...  This CLAIM is constructible not adiabatically, outside the adiabatic L only. ♣ Under the consistency of the system P, it is not possible to derive such a CLAIM that is stating this consistency supposition  ... 
doi:10.5772/intechopen.87975 fatcat:otnbq6lbhjf2lckuks4rdbwjp4

Adiabatic theorem for closed quantum systems initialized at finite temperature [article]

Nikolai Il`in, Anastasia Aristova, Oleg Lychkovskiy
2020 arXiv   pre-print
The celebrated quantum adiabatic theorem ensures that such pure state adiabaticity can be maintained with arbitrary accuracy, provided one chooses a small enough driving rate.  ...  The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian.  ...  The work was supported by the Russian Science Foundation under the grant N o 17-71-20158. [1] Max Born, "Das adiabatenprinzip in der quantenmeehanik,"  ... 
arXiv:2002.02947v3 fatcat:flxltqafhvdcpk622srra264qm

Geometry of the adiabatic theorem

Augusto César Lobo, Rafael Antunes Ribeiro, Clyffe de Assis Ribeiro, Pedro Ruas Dieguez
2012 European journal of physics  
We have chosen to use only the minimum geometric structure needed for an understanding of the adiabatic theorem for this case.  ...  We present a simple and pedagogical derivation of the quantum adiabatic theorem for two level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov  ...  The authors also wishes to thank the anonymous referee for many valuable suggestions that helped much to improve the quality of this manuscript.  ... 
doi:10.1088/0143-0807/33/5/1063 fatcat:mujtuhvzlvednnf6kapsxwn3cu

Fluctuation Theorem for a Small Engine and Magnetization Switching by Spin Torque

Yasuhiro Utsumi, Tomohiro Taniguchi
2015 Physical Review Letters  
We adopt the theory of the full-counting statistics under the adiabatic pumping of spin angular momentum.  ...  This enables us to account for the backaction effect, which is crucial to maintain consistency with the fluctuation theorem.  ...  We adopt the theory of the full-counting statistics under the adiabatic pumping of spin angular momentum.  ... 
doi:10.1103/physrevlett.114.186601 pmid:26001013 fatcat:v2chqq2oqjciroqwvtztcvemgi
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