Related papers: Adiabatic approximation, Gell-Mann and Low theorem…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
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 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…
This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert…
In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dimensional one. In this paper, we formulate a generic scheme…
We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the…
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution (H(epsilon…
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and…
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…
In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector…
The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic…
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…
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…
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…
We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…