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We give an elementary proof to Hasse theorem.

General Mathematics · Mathematics 2012-12-12 Jianhua Chen , Debiao He , Zhijin Hu , Yitao Chen , Hao Hu

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

Quantum Physics · Physics 2007-11-08 Sabine Jansen , Mary-Beth Ruskai , Ruedi Seiler

For slow--fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.

Mathematical Physics · Physics 2014-04-09 M. Karasev

Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…

Quantum Physics · Physics 2019-01-23 Jingwei Wen , Xiangyu Kong , Shijie Wei , Bixue Wang , Tao Xin , Guilu Long

The quantitative adiabatic condition (QAC), or quantitative condition, is a convenient (a priori) tool for estimating the adiabaticity of quantum evolutions. However, the range of the applicability of QAC is not well understood. It has been…

Quantum Physics · Physics 2014-05-13 Dafa Li , Man-Hong Yung

The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard…

Quantum Physics · Physics 2020-11-12 Alan C. Santos , Marcelo S. Sarandy

The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…

Quantum Physics · Physics 2009-11-10 D. M. Tong , K. Singh , L. C. Kwek , C. H. Oh

Quantum adiabatic computation is a novel paradigm for the design of quantum algorithms, which is usually used to find the minimum of a classical function. In this paper, we show that if the initial hamiltonian of a quantum adiabatic…

Quantum Physics · Physics 2007-05-23 Zhaohui Wei , Mingsheng Ying

The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning…

Quantum Physics · Physics 2011-02-02 Qian-Heng Duan , Ping-Xing Chen , Wei Wu

We construct a measure for the adiabatic contribution to quantum transitions in an arbitrary basis, tackling the generic complex case where dynamics is only partially adiabatic, simultaneously populates several eigenstates and transitions…

Quantum Physics · Physics 2025-04-08 R. Pant , P. K. Verma , C. Rangi , E. Mondal , M. Bhati , V. Srinivasan , S. Wüster

We examine the quantitative condition which has been widely used as a criterion for the adiabatic approximation but was recently found insufficient. Our results indicate that the usual quantitative condition is sufficient for a special…

Quantum Physics · Physics 2015-05-13 D M Tong , K Singh , L C Kwek , C H OH

We provide a simple proof of Kamp's theorem.

Logic in Computer Science · Computer Science 2015-07-01 Alexander Rabinovich

We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered…

Mathematical Physics · Physics 2015-06-22 David Viennot , Lucile Aubourg

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$…

Quantum Physics · Physics 2009-11-13 P. Ribeiro , R. Mosseri

We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building…

Quantum Physics · Physics 2015-02-19 Itay Hen

A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .

Quantum Physics · Physics 2011-04-15 W. Luecke

We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.

Quantum Physics · Physics 2007-05-23 Tien D. Kieu

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…

Quantum Physics · Physics 2016-05-12 Zhen-Yu Wang , Martin B. Plenio

An analytically solvable model for quasi-static transformations across quantum critical points featuring Bosonic quasi-particle excitations is presented. The model proves that adiabaticity breakdown is a general feature of universal slow…

Quantum Physics · Physics 2021-08-11 Nicolò Defenu

We outline an algorithm for the Quantum Counting problem using Adiabatic Quantum Computation (AQC). We show that using local adiabatic evolution, a process in which the adiabatic procedure is performed at a variable rate, the problem is…

Quantum Physics · Physics 2014-06-02 Itay Hen