Related papers: Berry Phase Estimation in Gate-Based Adiabatic Qua…
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…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are…
Implementation of quantum logical gates for multilevel system is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can…
A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator…
On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical…
We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the…
Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and…
We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the…
The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an…
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…
In this work we study the geometrical and topological properties of non-equilibrium quantum systems driven by ac fields. We consider two tunnel coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our…