67 research outputs found
Improved phase gate reliability in systems with neutral Ising anyons
Recent proposals using heterostructures of superconducting and either
topologically insulating or semiconducting layers have been put forth as
possible platforms for topological quantum computation. These systems are
predicted to contain Ising anyons and share the feature of having only neutral
edge excitations. In this note, we show that these proposals can be combined
with the recently proposed "sack geometry" for implementation of a phase gate
in order to conduct robust universal quantum computation. In addition, we
propose a general method for adjusting edge tunneling rates in such systems,
which is necessary for the control of interferometric devices. The error rate
for the phase gate in neutral Ising systems is parametrically smaller than for
a similar geometry in which the edge modes carry charge: it goes as
rather than at low temperatures. At zero temperature, the phase variance
becomes constant at long times rather than carrying a logarithmic divergence.Comment: 5 pages, 1 figur
Persistence of the flat band in a kagome magnet with dipolar interactions
The weathervane modes of the classical Heisenberg antiferromagnet on the
kagome lattice constitute possibly the earliest and certainly the most
celebrated example of a flat band of zero-energy excitations. Such modes arise
from the underconstraint that has since become a defining criterion of strong
geometrical frustration. We investigate the fate of this flat band when dipolar
interactions are added. These change the nearest-neighbour model fundamentally
as they remove the Heisenberg spin-rotational symmetry while also introducing a
long- range component to the interaction. We explain how the modes continue to
remain approximately dispersionless, while being lifted to finite energy as
well as being squeezed: they change their ellipticity described by the ratio of
the amplitudes of the canonically conjugate variables comprising them. This
phenomenon provides interesting connections between concepts such as constraint
counting and self-screening underpinning the field of frustrated magnetism. We
discuss variants of these phenomena for different interactions, lattices and
dimension.Comment: 12 pages, 7 figure
Reversible first-order transition in Pauli percolation
Percolation plays an important role in fields and phenomena as diverse as the
study of social networks, the dynamics of epidemics, the robustness of
electricity grids, conduction in disordered media, and geometric properties in
statistical physics. We analyse a new percolation problem in which the first
order nature of an equilibrium percolation transition can be established
analytically and verified numerically. The rules for this site percolation
model are physical and very simple, requiring only the introduction of a weight
for a cluster of size . This establishes that a discontinuous
percolation transition can occur with qualitatively more local interactions
than in all currently considered examples of explosive percolation; and that,
unlike these, it can be reversible. This greatly extends both the applicability
of such percolation models in principle, and their reach in practice.Comment: 4 pages + Supplementary Material
Exotic circuit elements from zero-modes in hybrid superconductor/quantum Hall systems
Heterostructures formed by quantum Hall systems and superconductors have
recently been shown to support widely coveted Majorana fermion zero-modes and
still more exotic `parafermionic' generalizations. Here we establish that
probing such zero-modes using quantum Hall edge states yields non-local
transport signatures that pave the way towards a variety of novel circuit
elements. In particular, we demonstrate quite generally that at low energies
the zero-modes convert chirally moving quasiparticles into oppositely charged
quasiholes propagating in the same direction---that is, they swap the sign of
the chiral edge currents. One may then construct new and potentially useful
circuit elements using this `perfect Andreev conversion' process, including
superconducting current and voltage mirrors as well as transistors for
fractional charge currents. Characterization of these circuit elements should
provide striking evidence of the zero-mode physics.Comment: 7 pages, 5 figures, v2: references adde
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