664 research outputs found
Convex Graph Invariant Relaxations For Graph Edit Distance
The edit distance between two graphs is a widely used measure of similarity
that evaluates the smallest number of vertex and edge deletions/insertions
required to transform one graph to another. It is NP-hard to compute in
general, and a large number of heuristics have been proposed for approximating
this quantity. With few exceptions, these methods generally provide upper
bounds on the edit distance between two graphs. In this paper, we propose a new
family of computationally tractable convex relaxations for obtaining lower
bounds on graph edit distance. These relaxations can be tailored to the
structural properties of the particular graphs via convex graph invariants.
Specific examples that we highlight in this paper include constraints on the
graph spectrum as well as (tractable approximations of) the stability number
and the maximum-cut values of graphs. We prove under suitable conditions that
our relaxations are tight (i.e., exactly compute the graph edit distance) when
one of the graphs consists of few eigenvalues. We also validate the utility of
our framework on synthetic problems as well as real applications involving
molecular structure comparison problems in chemistry.Comment: 27 pages, 7 figure
Theory of magnon motive force in chiral ferromagnets
We predict that magnon motive force can lead to temperature dependent,
nonlinear chiral damping in both conducting and insulating ferromagnets. We
estimate that this damping can significantly influence the motion of skyrmions
and domain walls at finite temperatures. We also find that in systems with low
Gilbert damping moving chiral magnetic textures and resulting magnon motive
forces can induce large spin and energy currents in the transverse direction
Parafermion stabilizer codes
We define and study parafermion stabilizer codes which can be viewed as
generalizations of Kitaev's one dimensional model of unpaired Majorana
fermions. Parafermion stabilizer codes can protect against low-weight errors
acting on a small subset of parafermion modes in analogy to qudit stabilizer
codes. Examples of several smallest parafermion stabilizer codes are given. A
locality preserving embedding of qudit operators into parafermion operators is
established which allows one to map known qudit stabilizer codes to parafermion
codes. We also present a local 2D parafermion construction that combines
topological protection of Kitaev's toric code with additional protection
relying on parity conservation
Stabilization and control of Majorana bound states with elongated skyrmions
We show that elongated magnetic skyrmions can host Majorana bound states in a
proximity-coupled two-dimensional electron gas sandwiched between a chiral
magnet and an -wave superconductor. Our proposal requires stable skyrmions
with unit topological charge, which can be realized in a wide range of
multilayer magnets, and allows quantum information transfer by using standard
methods in spintronics via skyrmion motion. We also show how braiding
operations can be realized in our proposal
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