Related papers: Adiabatic Theorem without a Gap Condition

We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its…

We study the adiabatic time evolution of quantum resonances over time scales which are small compared to the lifetime of the resonances. We consider three typical examples of resonances: The first one is that of shape resonances…

Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where…

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…

The accelerated optical lattice has emerged as a valuable technique for the investigation of quantum transport physics and has found widespread application in quantum sensing, including atomic gravimeters and atomic gyroscopes. In our…

We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum computation.

The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…

Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in…

The consistency of quantum adiabatic theorem has been doubted recently. It is shown in the present paper that the difference between the adiabatic solution and the exact solution to the Schrodinger equation with a slowly changing driving…

We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths…

One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation,…

Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…

The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that…

Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…

Conditional geometric phase shift gate, which is fault tolerate to certain errors due to its geometric property, is made by NMR technique recently under adiabatic condition. By the adiabatic requirement, the result is inexact unless the…

A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting…

We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of…

We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian $\mathcal{L}(t)$. We focus on the finite system case relevant for adiabatic…