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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.…

We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of…

Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…

In the experimental context of cold-fermion optical lattices, we discuss the possibilities to approach the pseudogap or ordered phases by manipulating the scattering length or the strength of the laser-induced lattice potential. Using the…

We study the folding of RNA secondary structures with quenched sequence randomness by means of the constrained annealing method. A thermodynamic phase transition is induced by including the conformational weight of loop structures. In…

We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations,…

We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak coupling…

Accurate and efficient quantum control in the presence of constraints and decoherence is a requirement and a challenge in quantum information processing. Shortcuts to adiabaticity, originally proposed to speed up slow adiabatic process,…

We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon…

We introduce a method where successive coordinate transformations are applied to decrease the error in the adiabatic master equation resulting from truncation in the local adiabatic parameter. Our method reduces the nonphysical behaviour…

A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$…

Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum…

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…

We consider a time-dependent two-level quantum system interacting with a free Boson reservoir. The coupling is energy conserving and depends slowly on time, as does the system Hamiltonian, with a common adiabatic parameter $\varepsilon$.…

High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. In electron spin resonance, manipulation of the quantum spin is usually achieved with time-dependent microwave fields. In contrast to…

Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and…

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in…

Traditional simulated annealing utilizes thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. We compare…

Quantum annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the…

We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…