740 research outputs found
A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores
quantum dynamics in a spin system as a precursor to a quantum theory of
gravity. The model has no a priori geometric properties, instead, locality is
inferred from the more fundamental notion of interaction between the matter
degrees of freedom. The interaction terms are themselves quantum degrees of
freedom so that the structure of interactions and hence the resulting local and
causal structures are dynamical. The system is a Hubbard model where the graph
of the interactions is a set of quantum evolving variables. We show
entanglement between spatial and matter degrees of freedom. We study
numerically the quantum system and analyze its entanglement dynamics. We
analyze the asymptotic behavior of the classical model. Finally, we discuss
analogues of trapped surfaces and gravitational attraction in this simple
model.Comment: 23 pages, 6 figures; updated to published versio
Interacting quantum walk on a graph
We introduce an elementary quantum system consisting of a set of spins on a
graph and a particle hopping between its nodes. The quantum state is build
sequentially, applying a unitary transformation that couples neighboring spins
and, at a node, the local spin with the particle. We observe the relaxation of
the system towards a stationary paramagnetic or ferromagnetic state, and
demonstrate that it is related to eigenvectors thermalization and random matrix
statistics. The relation between these macroscopic properties and interaction
generated entanglement is discussed.Comment: 15 pages, 11 figures (v2 extended version
Quantum simulation of the Anderson Hamiltonian with an array of coupled nanoresonators: delocalization and thermalization effects
The possibility of using nanoelectromechanical systems as a simulation tool
for quantum many-body effects is explored. It is demonstrated that an array of
electrostatically coupled nanoresonators can effectively simulate the
Bose-Hubbard model without interactions, corresponding in the single-phonon
regime to the Anderson tight-binding model. Employing a density matrix
formalism for the system coupled to a bosonic thermal bath, we study the
interplay between disorder and thermalization, focusing on the delocalization
process. It is found that the phonon population remains localized for a long
time at low enough temperatures; with increasing temperatures the localization
is rapidly lost due to thermal pumping of excitations into the array, producing
in the equilibrium a fully thermalized system. Finally, we consider a possible
experimental design to measure the phonon population in the array by means of a
superconducting transmon qubit coupled to individual nanoresonators. We also
consider the possibility of using the proposed quantum simulator for realizing
continuous-time quantum walks.Comment: Replaced with new improved version. To appear in EPJ Q
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic
excitations and are coupled to a thermal bath. We propose a phenomenological
model for the resulting short-time dynamics that includes pair-creation,
hopping, braiding, and fusion of anyons. By explicitly constructing topological
quantum error-correcting codes for this class of system, we use our
thermalization model to estimate the lifetime of the quantum information stored
in the encoded spaces. To decode and correct errors in these codes, we adapt
several existing topological decoders to the non-Abelian setting. We perform
large-scale numerical simulations of these two-dimensional Ising anyon systems
and find that the thresholds of these models range between 13% to 25%. To our
knowledge, these are the first numerical threshold estimates for quantum codes
without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a
misstatement about the detailed balance condition of our Metropolis
simulations. All conclusions from v1 are unaffected by this correctio
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