3,460 research outputs found
Creation of two-dimensional coulomb crystals of ions in oblate Paul traps for quantum simulations
We develop the theory to describe the equilibrium ion positions and phonon
modes for a trapped ion quantum simulator in an oblate Paul trap that creates
two-dimensional Coulomb crystals in a triangular lattice. By coupling the
internal states of the ions to laser beams propagating along the symmetry axis,
we study the effective Ising spin-spin interactions that are mediated via the
axial phonons and are less sensitive to ion micromotion. We find that the axial
mode frequencies permit the programming of Ising interactions with inverse
power law spin-spin couplings that can be tuned from uniform to with
DC voltages. Such a trap could allow for interesting new geometrical
configurations for quantum simulations on moderately sized systems including
frustrated magnetism on triangular lattices or Aharonov-Bohm effects on ion
tunneling. The trap also incorporates periodic boundary conditions around loops
which could be employed to examine time crystals.Comment: 17 pages, 8 figures, submitted to the journal EPJ Quantum Technology
for the thematic Series on Quantum Simulation
Lazy Model Expansion: Interleaving Grounding with Search
Finding satisfying assignments for the variables involved in a set of
constraints can be cast as a (bounded) model generation problem: search for
(bounded) models of a theory in some logic. The state-of-the-art approach for
bounded model generation for rich knowledge representation languages, like ASP,
FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or
propositional one and apply a search algorithm to the resulting theory.
An important bottleneck is the blowup of the size of the theory caused by the
reduction phase. Lazily grounding the theory during search is a way to overcome
this bottleneck. We present a theoretical framework and an implementation in
the context of the FO(.) knowledge representation language. Instead of
grounding all parts of a theory, justifications are derived for some parts of
it. Given a partial assignment for the grounded part of the theory and valid
justifications for the formulas of the non-grounded part, the justifications
provide a recipe to construct a complete assignment that satisfies the
non-grounded part. When a justification for a particular formula becomes
invalid during search, a new one is derived; if that fails, the formula is
split in a part to be grounded and a part that can be justified.
The theoretical framework captures existing approaches for tackling the
grounding bottleneck such as lazy clause generation and grounding-on-the-fly,
and presents a generalization of the 2-watched literal scheme. We present an
algorithm for lazy model expansion and integrate it in a model generator for
FO(ID), a language extending first-order logic with inductive definitions. The
algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base
System IDP. Experimental results illustrate the power and generality of the
approach
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