Related papers: Towards generic adiabatic elimination for bipartit…
We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with $\mathbb{S}^1 -$symmetry.…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its…
We apply the method of shortcuts to adiabaticity to nonequilibrium systems. For unitary dynamics, the system Hamiltonian is separated into two parts. One of them defines the adiabatic states for the state to follow and the nonadiabatic…
We propose a new set of equations to determine the collective Hamiltonian including the second-order collective-coordinate operator on the basis of the adiabatic self-consistent collective-coordinate (ASCC) theory. We illustrate, with the…
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialised state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible.…
In open quantum systems theory, reduced models are invaluable for conceptual understanding and computational efficiency. Adiabatic elimination is a useful model reduction method for systems with separated timescales, where a reduced model…
We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground…
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through…
It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic…
Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…
We discuss dynamics of periodically-driven open quantum systems. The time evolution of the quantum state is described by the quantum master equation and the form of the dissipator is chosen so that the instantaneous stationary state is…
Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator,…
In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…
Adiabatic modes are cosmological perturbations that are locally indistinguishable from a (large) change of coordinates. At the classical level, they provide model independent solutions. At the quantum level, they lead to soft theorems for…
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…
We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport,…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…