Related papers: Eternal Adiabaticity
The analytical expression for shortcuts to adiabaticity for any switching time and any thermally isolated system performing a finite-time and weakly driven process is presented. It is based on the analytical solution of the optimal…
The quantum adiabatic theorem is a fundamental result in quantum mechanics, with a multitude of applications, both theoretical and practical. Here, we investigate the dynamics of adiabatic processes for quantum many-body systems %in detail…
Adiabaticity of quantum evolution is important in many settings. One example is the adiabatic quantum computation. Nevertheless, up to now, there is no effective method to test the adiabaticity of the evolution when the eigenenergies of the…
We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum…
We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for…
We prove a robust extension of the quantum adiabatic theorem. The theorem applies to systems that have resonances instead of bound states, and to systems for which just an approximation to a bound state is known. To demonstrate the…
We prove that, for a quantum system that undergoes a strong perturbation, the solution of the leading order equation of the strong field approximation (M.Frasca, Phys. Rev. A, {\bf 45}, 43 (1992)) can be derived by the adiabatic…
The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state which tends to the solution [Farhi et al.,…
We prove an adiabatic theorem that applies at timescales short of the typical adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of…
We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature $\beta$. The time evolution is discrete and such that over each time step of…
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of…
We prove an adiabatic theorem for infinitely extended lattice fermion systems with gapped ground states, allowing perturbations that may close the gap. The Heisenberg dynamics on the CAR-algebra is generated by a time dependent…
We consider the simplest example of a nonstationary quantum system which is quantum mechanical oscillator with varying frequency and $\lambda \phi^4$ self-interaction. We calculate loop corrections to the Keldysh, retarded/advanced…
We develop new protocols for high-fidelity single qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures with highly isolated logical states, where…
A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…
We construct an extensive adiabatic invariant for a Klein-Gordon chain in the thermodynamic limit. In particular, given a fixed and sufficiently small value of the coupling constant $a$, the evolution of the adiabatic invariant is…
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the…
We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…