9,927 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
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
Exotic non-Abelian anyons from conventional fractional quantum Hall states
Non-Abelian anyons--particles whose exchange noncommutatively transforms a
system's quantum state--are widely sought for the exotic fundamental physics
they harbor as well as for quantum computing applications. There now exist
numerous blueprints for stabilizing the simplest type of non-Abelian anyon,
defects binding Majorana modes, by judiciously interfacing widely available
materials. Following this line of attack, we introduce a device fabricated from
conventional fractional quantum Hall states and s-wave superconductors that
supports exotic non-Abelian anyons that bind `parafermions', which can be
viewed as fractionalized Majorana fermions. We show that these modes can be
experimentally identified (and distinguished from Majoranas) using Josephson
measurements. We also provide a practical recipe for braiding parafermions and
show that they give rise to non-Abelian statistics. Interestingly, braiding in
our setup produces a richer set of topologically protected qubit operations
when compared to the Majorana case. As a byproduct, we establish a new,
experimentally realistic Majorana platform in weakly spin-orbit-coupled
materials such as GaAs.Comment: 12 pages, 4 figure
A practical phase gate for producing Bell violations in Majorana wires
The Gottesman-Knill theorem holds that operations from the Clifford group,
when combined with preparation and detection of qubit states in the
computational basis, are insufficient for universal quantum computation.
Indeed, any measurement results in such a system could be reproduced within a
local hidden variable theory, so that there is no need for a quantum mechanical
explanation and therefore no possibility of quantum speedup. Unfortunately,
Clifford operations are precisely the ones available through braiding and
measurement in systems supporting non-Abelian Majorana zero modes, which are
otherwise an excellent candidate for topologically protected quantum
computation. In order to move beyond the classically simulable subspace, an
additional phase gate is required. This phase gate allows the system to violate
the Bell-like CHSH inequality that would constrain a local hidden variable
theory. In this article, we both demonstrate the procedure for measuring Bell
violations in Majorana systems and introduce a new type of phase gate for the
already existing semiconductor-based Majorana wire systems. We conclude with an
experimentally feasible schematic combining the two, which should potentially
lead to the demonstration of Bell violation in a Majorana experiment in the
near future. Our work also naturally leads to a well-defined platform for
universal fault-tolerant quantum computation using Majorana zero modes, which
we describe.Comment: 11 pages, 13 figures; Title and references update
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