IFUAP

We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to external perturbation. The scaling of errors with system parameters and number of qubits is explained. We use two different procedures to fight each of them. To suppress spurious transitions we use correcting pulses (generalized 2πk method) while to suppress errors due to external perturbation we use an improved QFT algorithm. As a result, the fidelity of quantum computation is increased by several orders of magnitude and is thus stable in a much wider range of physical parameters.

A one dimensional Classical Heisenberg Model, with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as ergodicity and chaoticity are strongly different. Indeed, even in presence of chaoticity, the model displays a lack of ergodicity only in the case of all-to-all interaction and below an energy threshold, that persists in the thermodynamical (infinite size) limit. This energy threshold, which we called the non-ergodicity threshold, can be found analytically and results can be generalized for a generic Classical Heisenberg Model with asymmetric coupling. Also the case in which the interaction potential decays as R −α is discussed. We prove that for α > 1 (shor-range case) the non-ergodicity threshold does not exist. For α < 1, except the infinite range case (α = 0), the question of the existence of the non-ergodicity threshold is still open. We conjectured that it exists for the long-range case. The issue of the relevance of the non-ergodicity threshold with respect to phase transitions has also been addressed. Below the non-ergodicity threshold, the energy surface is disconnected in two components with positive and negative magnetizations respectively. Because the dynamics is continous this implies that magnetization cannot change sign in time below the non-ergodicity threshold. Above the threshold, in a fully chaotic regime, magnetization changes sign in a stochastic way and its behavior can be fully characterized by an average magnetization reversal time. Statistical mechanics predicts a phase-transition at an energy higher than the ergodicity threshold. We assess the dynamical relevance of the latter for finite size systems through numerical simulations and analytical calculations. In particular, we derive an explicit expression of the time scale for magnetic reversal. As for standard phase transitions, this time-scale, as a function of the energy, diverges as a power at the non-ergodicity threshold. Moreover it increases exponentially with N . We also analyze the behavior of the system when the dynamics is not fully chaotic, for suitable values of the interaction strenght. In this quasi-integrable regime reversal times are strongly dependent on the initial conditions. The same system has also been studied from a quantum mechanical point of view. We address the problem of finding a quantum signature of the classical non-ergodicity threshold. Analysing the spectral properties of the system we define a quantum non-ergodicity threshold, in close correspondence with the classical one. We analyze the dynamical relevance of this threshold with respect to magnetic reversal times. We also show that, due to the existence of the non-ergodicity threshold, the interesting phenomena of Macroscopic Quantum Tunneling and Macroscopic Quantum Coherence can be found in the quantum case.

We analyze from the dynamical point of view the classical characteristics of the Topological Non-connectivity Threshold (TNT), recently introduced in F.Borgonovi, G.L.Celardo, M.Maianti, E.Pedersoli, J. Stat. Phys., 116, 516 (2004). This shows interesting connections among Topology, Dynamics, and Thermo-Statistics of ferro/paramagnetic phase transition in classical spin systems, due to the combined effect of anisotropy and long-range interections.

PACS 73.23.-b -Electronic transport in mesoscopic systems PACS 24.60.Lz -Chaos in nuclear systems PACS 21.60.-n -Nuclear structure models and methods Abstract -The model of an open Fermi system is used for studying the interplay of intrinsic chaos and irreversible decay into open continuum channels. Two versions of the model are characterized by one-body chaos coming from disorder or by many-body chaos due to the inter-particle interactions. The continuum coupling is described by the effective non-Hermitian Hamiltonian. Our main interest is in specific correlations of cross-sections for various channels in dependence on the coupling strength and degree of internal chaos. The results are generic and refer to common features of various mesoscopic objects including conductance fluctuations and resonance nuclear reactions.

Using an energy-independent non-Hermitian Hamiltonian approach to open systems, we fully describe transport through a sequence of potential barriers as external barriers are varied. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian model, a transition to a superradiant regime is shown to occur. Transport properties undergo a strong change at the superradiance transition, where the transmission is maximized and a drastic change in the structure of resonances is demonstrated. Finally, we analyze the effect of the superradiance transition in the Anderson localized regime.

Anisotropic Heisenberg models are characterized by an interesting feature depending on their energy value: below some energy threshold their phase space is topologically divided into two separate branches that cannot be connected by dynamical paths. The existence of such an energy threshold, called at the beginning the nonergodicity threshold, 1 but later2, 3 the topological nonconnectivity threshold TNT, has been proved for a class of classical Heisenberg models with anisotropic coupling and infinite range of interaction.

The degree of opening affects the properties of a system in an highly non trivial manner. An example of this is the phenomenon of Superradiance: in a typical situation, we have a discrete quantum system coupled to an external environment characterized by a continuum of

A one dimensional Classical Heisenberg Model, with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as ergodicity and chaoticity are strongly different. Indeed, even in presence of chaoticity, the model displays a lack of ergodicity only in the case of all-to-all interaction and below an energy threshold, that persists in the thermodynamical (infinite size) limit. This energy threshold, which we called the non-ergodicity threshold, can be found analytically and results can be generalized for a generic Classical Heisenberg Model with asymmetric coupling. Also the case in which the interaction potential decays as R −α is discussed. We prove that for α > 1 (shor-range case) the non-ergodicity threshold does not exist. For α < 1, except the infinite range case (α = 0), the question of the existence of the non-ergodicity threshold is still open. We conjectured that it exists for the long-range case. The issue of the relevance of the non-ergodicity threshold with respect to phase transitions has also been addressed. Below the non-ergodicity threshold, the energy surface is disconnected in two components with positive and negative magnetizations respectively. Because the dynamics is continous this implies that magnetization cannot change sign in time below the non-ergodicity threshold. Above the threshold, in a fully chaotic regime, magnetization changes sign in a stochastic way and its behavior can be fully characterized by an average magnetization reversal time. Statistical mechanics predicts a phase-transition at an energy higher than the ergodicity threshold. We assess the dynamical relevance of the latter for finite size systems through numerical simulations and analytical calculations. In particular, we derive an explicit expression of the time scale for magnetic reversal. As for standard phase transitions, this time-scale, as a function of the energy, diverges as a power at the non-ergodicity threshold. Moreover it increases exponentially with N . We also analyze the behavior of the system when the dynamics is not fully chaotic, for suitable values of the interaction strenght. In this quasi-integrable regime reversal times are strongly dependent on the initial conditions. The same system has also been studied from a quantum mechanical point of view. We address the problem of finding a quantum signature of the classical non-ergodicity threshold. Analysing the spectral properties of the system we define a quantum non-ergodicity threshold, in close correspondence with the classical one. We analyze the dynamical relevance of this threshold with respect to magnetic reversal times. We also show that, due to the existence of the non-ergodicity threshold, the interesting phenomena of Macroscopic Quantum Tunneling and Macroscopic Quantum Coherence can be found in the quantum case.

An open multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport, both with and without intrinsic disorder. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy band. In the open system, using the method of the effective non-Hermitian Hamiltonian, we study signal transmission through such a circuit, with an important result of a long lifetime of localized states. When the average level width becomes comparable to the mean level spacing, the super-radiant transition occurs. In the case of on-site disorder we find an analytical estimate, confirmed by numerical data, for the robustness of the isolated states and their role in transport processes.

We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super-and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench superradiance. We identify two different regimes: (i) weak opening, in which superradiance is quenched at the same critical disorder at which the states of the closed system localize; (ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.

We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super-and subradiant behavior. Moreover, each two-level system is coupled to another independent environment, modeled by a classical white noise, simulating a dephasing bath and described by the Haken-Strobl master equation. Single-exciton superradiance, an example of a cooperative quantum coherent effect, is destroyed at a critical dephasing strength proportional to the system size, showing robustness of cooperativity to the action of the dephasing environment. We also show that the coupling to a common decay channel contrasts with the action of dephasing, driving the entanglement decay to slow down on increasing the system size. Moreover, after a projective measurement which finds the excitation in the system, the entanglement reaches a stationary value, independent of the initial conditions.