Related papers: An Elementary Proof of the Quantum Adiabatic Theor…
We give an elementary proof to Hasse theorem.
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.
For slow--fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.
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…
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…
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…
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 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…
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…
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…
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…
We provide a simple proof of Kamp's theorem.
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…
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 $\alpha$…
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…
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 .
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.
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…
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…
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…