Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

Long-range multipartite entanglement close to a first-order quantum phase transition

We provide insight into the quantum correlations structure present in strongly correlated systems beyond the standard framework of bipartite entanglement. To this aim we first exploit rotationally invariant states as a test bed to detect genuine tripartite entanglement beyond the nearest neighbor in spin-1/2 models. Then we construct in a closed analytical form a family of entanglement witnesses which provides a sufficient condition to determine if a state of a many-body system formed by an arbitrary number of spin-1/2 particles possesses genuine tripartite entanglement, independently of the details of the model. We illustrate our method by analyzing in detail the anisotropic XXZ spin chain close to its phase transitions, where we demonstrate the presence of long-range multipartite entanglement near the critical point and the breaking of the symmetries associated with the quantum phase transition.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

Scaling of magneto-quantum-radiative hydrodynamic equations: From laser-produced plasmas to astrophysics

We introduce the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.

Characterization of Bose-Hubbard models with quantum nondemolition measurements

We propose a scheme for the detection of quantum phase transitions in the one-dimensional (1D) Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the nondemolition measurement technique of quantum polarization spectroscopy. We use collective measurements of the effective total angular momentum of a particular spatial mode to characterize the Mott insulator to superfluid phase transition in the BH model and the transition to a density wave state in the EBH model. We extend the application of collective measurements to the ground states at various deformations of a superlattice potential.

Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.

Transitionless quantum driving in open quantum systems

We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the control strategy required to achieve superadiabaticity. We apply our formalism to two examples consisting of a two-level system coupled to environments with time-dependent bath operators. 

Correlation approach to work extraction from finite quantum systems

Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply the creation of quantum correlations, as measured by quantum discord. We also reanalyze the conditions under which global transformations outperform local gates as far as maximal work extraction is considered by deriving a necessary and sufficient condition that is based on classical correlations.

Localizationlike effect in two-dimensional alternate quantum walks with periodic coin operations

Exploiting multidimensional quantum walks as feasible platforms for quantum computation and quantum simulation attracts constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional quantum walk scheme with a single-qubit coin that presents, in the considered regimes, a strong localizationlike effect on the walker. The result could provide new possible directions for the implementation of quantum algorithms or from the point of view of quantum simulation. We characterize the localizationlike effect in terms of the parameters of a step-dependent qubit operation that acts on the coin space after any standard coin operation, showing that a proper choice can guarantee a nonnegligible probability of finding the walker in the origin even for large times. We finally discuss the robustness to imperfections, a qualitative relation with coherences behavior, and possible experimental realizations of this model with the current state-of-the-art settings.

Out-of-equilibrium thermodynamics of quantum optomechanical systems

We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full charac- terization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.

Hybrid optomechanics for Quantum Technologies

We review the physics of hybrid optomechanical systems consisting of a mechanical oscillator interacting with both a radiation mode and an additional matterlike system. We concentrate on the cases embodied by either a single or a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a wide range of physical effects, from passive mechanical cooling to the set-up of multipartite entanglement, from optomechanical nonlocality to the achievement of non-classical states of a single mechanical mode. The reviewed material showcases the viability of hybridised cavity optomechanical systems as basic building blocks for quantum communication networks and quantum state-engineering devices, possibly empowered by the use of quantum and optimal control techniques. The results that we discuss are instrumental to the promotion of hybrid optomechanical devices as promising experimental platforms for the study of nonclassicality at the genuine mesoscopic level.

Measuring work and heat in ultracold quantum gases

We propose a feasible experimental scheme to direct measure heat and work in cold atomic setups. The method is based on a recent proposal which shows that work is a positive operator valued measure (POVM). In the present contribution, we demonstrate that the interaction between the atoms and the light polarization of a probe laser allows us to implement such POVM. In this way the work done on or extracted from the atoms after a given process is encoded in the light quadrature that can be measured with a standard homodyne detection. The protocol allows one to verify fluctuation theorems and study properties of the non-unitary dynamics of a given thermodynamic process.

Cavity-aided quantum parameter estimation in a bosonic double-well Josephson junction

We describe an apparatus designed to make non-demolition measurements on a Bose-Einstein condensate (BEC) trapped in a double-well optical cavity. This apparatus contains, as well as the bosonic gas and the trap, an optical cavity. We show how the interaction between the light and the atoms, under appropriate conditions, can allow for a weakly disturbing yet highly precise measurement of the population imbalance between the two wells and its variance. We show that the setting is well suited for the implementation of quantum-limited estimation strategies for the inference of the key parameters defining the evolution of the atomic system and based on measurements performed on the cavity field. This would enable {\it de facto} Hamiltonian diagnosis via a highly controllable quantum probe.

Amplitude modulation of quantum-ion-acoustic wavepackets in electron-positron-ion plasmas: Modulational instability, envelope modes, extreme waves

A semirelativistic fluid model is employed to describe the nonlinear amplitude modulation of low-frequency (ionic scale) electrostatic waves in an unmagnetized electron-positron-ion plasma. Electrons and positrons are assumed to be degenerated and inertialess, whereas ions are warm and classical. A multiscale perturbation method is used to derive a nonlinear Schrödinger equation for the envelope amplitude, based on which the occurrence of modulational instability is investigated in detail. Various types of localized ion acoustic excitations are shown to exist, in the form of either bright type envelope solitons (envelope pulses) or dark-type envelope solitons (voids, holes). The plasma configurational parameters (namely, the relativistic degeneracy parameter, the positron concentration, and the ionic temperature) are shown to affect the conditions for modulational instability significantly, in fact modifying the associated threshold as well as the instability growth rate. In particular, the relativistic degeneracy parameter leads to an enhancement of the modulational instability mechanism. Furthermore, the effect of different relevant plasma parameters on the characteristics (amplitude, width) of these envelope solitary structures is also presented in detail. Finally, the occurrence of extreme amplitude excitation (rogue waves) is also discussed briefly. Our results aim at elucidating the formation and dynamics of nonlinear electrostatic excitations in superdense astrophysical regimes.

SIMLA: Simulating particle dynamics in intense laser and other electromagnetic fields via classical and quantum electrodynamics

We present the Fortran program SIMLA, which is designed for the study of charged particle dynamics in laser and other background fields. The dynamics can be determined classically via the Lorentz force and Landau–Lifshitz equations or, alternatively, via the simulation of photon emission events determined by strong-field quantum-electrodynamics amplitudes and implemented using Monte-Carlo routines. Multiple background fields can be included in the simulation and, where applicable, the propagation direction, field type (plane wave, focussed paraxial, constant crossed, or constant magnetic), and time envelope of each can be independently specified.