Related papers: Two kinds of quantum adiabatic approximation
Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is…
The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved…
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is…
We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of…
We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
For slow--fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.
Marzlin and Sanders \cite{marzlin} have shown rigorously that the adiabatic approximation can be very inaccurate when applied to a Hamiltonian $H(t)$ that generates the evolution $U^{\dagger} (t)$ even if it gives an excellent approximation…
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…
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 usual quantitative condition has been widely used in the practical applications of the adiabatic theorem. However, it had never been proved to be sufficient or necessary before. It was only recently found that the quantitative condition…
We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born--Oppenheimer approximations.
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one…
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations…