Sergio De Filippo

Quantum computation using decoherence-free states of the physical operator algebra

The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole-system algebra. If the physical algebra commutes with the interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary terms either commuting with or belonging to the physical algebra, then its states are decoherence free. One of the examples considered shows that, for a uniform collective coupling to the environment, the smallest number of physical qubits encoding a decoherence-free logical qubit is reduced from four to three.

A geometrical setting for the Lax representation

Abstract A geometrical interpretation of the Lax representation is suggested; it is read as the condition on a section of a fiber bundle based on the phase manifold to be covariantly constant, with respect to a suitable connection, along the dynamics.

Nonunitary higher derivative gravity classically equivalent to Einstein gravity and its Newtonian limit

Runaway solutions can be avoided in fourth order gravity by a doubling of the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with the change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its non-unitary Newtonian limit is compatible with the wavelike properties of microscopic particles and the classical behavior of macroscopic bodies, as well as with a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and black hole entropy emerges as entanglement entropy with hidden degrees of freedom.

Flat connections for nonlinear evolution equations

Abstract A geometrical setting for Lax representations of hierarchies of integrable nonlinear evolution equations is analyzed. Once the Lax operator L [ u ] is identified with a section of an associated bundle of a principal bundle based on phase manifold, Lax equations are read as parallel transport conditions for L [ u ] with respect to a connection with vanishing curvature.

A microscopic bosonization procedure of the chiral edge field theory for Laughlin states

Abstract A unified microscopic bosonization of the edge chiral field theory both for the Integer Quantum Hall Effect and the Laughlin wavefunction is given, without relying on the corresponding classical plasma. The edge excitations for the Laughlin wavefunction are adiabatically constructed starting from those of the integer case.

Adiabatic heuristic construction of trial wave functions for quantum Hall states at arbitrary fractional fillings

Abstract Starting from a lowest Landau level filled with several electron species, adiabatic interpolation through anyon hamiltonians is considered. The antisymmetrized final states are explicitriial wave functions for identical electrons, depending on three integer parameters, and generalize the Laughlin wave function to arbitrary fractional fillings. Space Carlo simulations. Numerical results are consistent with energies reported by other authors using much less simple trial wave functions.

A generalized discrete self-trapping equation as a model for quantum chaology

Abstract A generalisation of the discrete self-trapping (DST) Hamiltonian is presented. It is shown to be as good as the traditional one to study quantum ergodicity far from the uncoupled limit, while it is also suitable to be used in the near integrability regime, where the conventional DST Hamiltonian fails due to its non-genericity.

Exact zero energy bound states of a model potential for quantum dots

Abstract A model potential for quantum dots is introduced starting from its classical property of having a constant positive curvature Jacobi metric for its zero energy orbits, which prove to be circles. Starting from a generalized quantum symmetry, exact values of the well deepness are found for which normalizable zero energy eigenfunctions, whose analytic expressions is given, exist, by which a complete characterization of the bound state spectrum is given.

Chiral boson field theory for neutral and charged edge excitations of Laughlin liquids in smooth confining potentials

Abstract A microscopic construction of the chiral boson edge field theory for neutral and charged excitations of generalized Laughlins states in smooth confining potentials for two-edge geometries is described. This is done by taking account of the topological degrees of freedom of the two chiral fields, which obey a joint constraint due to overall neutrality. This establishes a thorough correspondence with some traits of the heterotic string construction.

A commutative setting for integrable theories with fermions

Abstract Graded versions of the KdV equation are shown to be equivalent to traditional hamiltonian field theories without anticommuting variables. The explicit examples here given illustrate a general procedure, which can be applied not only to super-integrable, but also to more general theories with fermions. Supersymmetry transformations are shown to correspond, in the proposed setting, to ordinary hamiltonian symmetries.