27 research outputs found
A Formulation of Lattice Gauge Theories for Quantum Simulations
We examine the Kogut-Susskind formulation of lattice gauge theories under the
light of fermionic and bosonic degrees of freedom that provide a description
useful to the development of quantum simulators of gauge invariant models. We
consider both discrete and continuous gauge groups and adopt a realistic
multi-component Fock space for the definition of matter degrees of freedom. In
particular, we express the Hamiltonian of the gauge theory and the Gauss law in
terms of Fock operators. The gauge fields are described in two different bases,
based on either group elements or group representations. This formulation
allows for a natural scheme to achieve a consistent truncation of the Hilbert
space for continuous groups, and provides helpful tools to study the
connections of gauge theories with topological quantum double and string-net
models for discrete groups. Several examples, including the case of the
discrete gauge group, are presented.Comment: 13 pages, 1 figur
Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
We show that non-abelian potentials acting on ultracold gases with two
hyperfine levels can give rise to ground states with non-abelian excitations.
We consider a realistic gauge potential for which the Landau levels can be
exactly determined: the non-abelian part of the vector potential makes the
Landau levels non-degenerate. In the presence of strong repulsive interactions,
deformed Laughlin ground states occur in general. However, at the degeneracy
points of the Landau levels, non-abelian quantum Hall states appear: these
ground states, including deformed Moore-Read states (characterized by Ising
anyons as quasi-holes), are studied for both fermionic and bosonic gases.Comment: Published versio
Topological Quantum Computation, Anyons and non-Abelian Gauge Potentials
This thesis deals with the study of topological quantum computation and the possible realization of non-Abelian anyons in cold atomic gases. Two main topics are investigated:
the first subject is the quantum hashing technique to approximate unitary operators by
braiding non-Abelian anyons, the second one is the analysis of systems of multicomponent
ultracold atoms in the presence of an effective non-Abelian gauge potential giving rise to a
quantum Hall regime. The common frame of these topics is the emergent study of topological
phases of matters, driven by the necessity to overcome the Landau-Ginzburg paradigm
to describe strongly correlated quantum systems such as the quantum Hall ones. To achieve
this goal it is crucial to involve seemingly distant branches of knowledge such as conformal
field theories, topological field theories, integrable models, knot theory, tensor category
theory but also quantum information and computation, in order to deepen our understanding
of the new and exciting experimental and numerical results given by the analysis of different
systems sharing these topological properties
Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
Tensor networks, and in particular Projected Entangled Pair States (PEPS),
are a powerful tool for the study of quantum many body physics, thanks to both
their built-in ability of classifying and studying symmetries, and the
efficient numerical calculations they allow. In this work, we introduce a way
to extend the set of symmetric PEPS in order to include local gauge invariance
and investigate lattice gauge theories with fermionic matter. To this purpose,
we provide as a case study and first example, the construction of a fermionic
PEPS, based on Gaussian schemes, invariant under both global and local U(1)
gauge transformations. The obtained states correspond to a truncated U(1)
lattice gauge theory in 2 + 1 dimensions, involving both the gauge field and
fermionic matter. For the global symmetry (pure fermionic) case, these PEPS can
be studied in terms of spinless fermions subject to a p-wave superconducting
pairing. For the local symmetry (fermions and gauge fields) case, we find
confined and deconfined phases in the pure gauge limit, and we discuss the
screening properties of the phases arising in the presence of dynamical matter
Dissemination activity and impact of maternal and newborn health projects in Ethiopia, India and Nigeria
This study aimed to document the key messages, dissemination activities and impacts of selected projects within the Bill & Melinda Gates Foundation Maternal, Neonatal and Child Health strategy portfolio, and consider how these might contribute toward the learning agenda for the strategy
The resonant state at filling factor ν = 1/2 in chiral fermionic ladders
Helical liquids have been experimentally realized in both nanowires and ultracold atomic chains as the result of strong spin–orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as chiral synthetic ladders, with artificial magnetic fluxes determined by the spin–orbit terms. In this work, we characterize the helical state which appears at filling ν = 1/2: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states
Multi-level effects in quantum-dot based parity-to-charge conversion of Majorana box qubits
Quantum-dot based parity-to-charge conversion is a promising method for
reading out quantum information encoded nonlocally into pairs of Majorana zero
modes. To obtain a sizable parity-to-charge visibility, it is crucial to tune
the relative phase of the tunnel couplings between the dot and the Majorana
modes appropriately. However, in the presence of multiple quasi-degenerate dot
orbitals, it is in general not experimentally feasible to tune all couplings
individually. This paper shows that such configurations could make it difficult
to avoid a destructive multi-orbital interference effect that substantially
reduces the read-out visibility. We analyze this effect using a Lindblad
quantum master equation. This exposes how the experimentally relevant system
parameters enhance or suppress the visibility when strong charging energy,
measurement dissipation and, most importantly, multi-orbital interference is
accounted for. In particular, we find that an intermediate-time readout could
mitigate some of the interference-related visibility reductions affecting the
stationary limit.Comment: 10 pages + 5 pages appendix/references, 9 figure