Related papers: Geometry of an adiabatic passage at a level crossi…
We propose a new variant of the controlled-NOT quantum logic gate based on adiabatic level-crossing dynamics of the q-bits. The gate has a natural implementation in terms of the Cooper pair transport in arrays of small Josephson tunnel…
In this paperwe propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques…
We construct a measure for the adiabatic contribution to quantum transitions in an arbitrary basis, tackling the generic complex case where dynamics is only partially adiabatic, simultaneously populates several eigenstates and transitions…
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…
Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a…
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…
We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…
We consider non-adiabatic transitions in multiple dimensions, which occur when the Born-Oppenheimer approximation breaks down. We present a general, multi-dimensional algorithm which can be used to accurately and efficiently compute the…
The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
We present a means of studying rare reactive pathways in open quantum systems using Transition Path Theory and ensembles of quantum jump trajectories. This approach allows for elucidation of reactive paths for dissipative, nonadiabatic…
We analyse the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time dependent couplings which represent the…
We study state conversion in parity-time (PT) symmetry broken non-Hermitian two level system. We construct a theory and explain underlying mechanism for state conversion and define adiabatic evolutions in non-Hermitian systems. The…
It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching.…
The development of advanced quantum technologies and the quest for a deeper understanding of many-particle quantum mechanics requires control over the quantum state of interacting particles to a high degree of fidelity. However, the quickly…
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…
Nonadiabatic holonomic quantum computation uses non-Abelian geometric phases to implement a universal set of quantum gates that are robust against control imperfections and decoherence. Until now, a number of three-level-based schemes of…
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…
Unavoided crossings of the energy levels due to a variation of a real parameter are studied. It is found that after the quantum system in question passes through one of its energy-crossing points {\it alias} Kato's exceptional points (EP),…
Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behaviour of a system under parameter variation can differ…