568 research outputs found
Topological quantum computation away from the ground state with Majorana fermions
We relax one of the requirements for topological quantum computation with
Majorana fermions. Topological quantum computation was discussed so far as
manipulation of the wave function within degenerate many body ground state. The
simplest particles providing degenerate ground state, Majorana fermions, often
coexist with extremely low energy excitations, so keeping the system in the
ground state may be hard. We show that the topological protection extends to
the excited states, as long as the Majorana fermions do not interact neither
directly, nor via the excited states. This protection relies on the fermion
parity conservation, and so it is generic to any implementation of Majorana
fermions.Comment: 3 pages, published versio
An attractive critical point from weak antilocalization on fractals
We report a new attractive critical point occurring in the Anderson
localization scaling flow of symplectic models on fractals. The scaling theory
of Anderson localization predicts that in disordered symplectic two-dimensional
systems weak antilocalization effects lead to a metal-insulator transition.
This transition is characterized by a repulsive critical point above which the
system becomes metallic. Fractals possess a non-integer scaling of conductance
in the classical limit which can be continuously tuned by changing the fractal
structure. We demonstrate that in disordered symplectic Hamiltonians defined on
fractals with classical conductance scaling , for , the metallic phase is replaced
by a critical phase with a scale invariant conductance dependent on the fractal
dimensionality. Our results show that disordered fractals allow an explicit
construction and verification of the expansion
Orbital effect of magnetic field on the Majorana phase diagram
Studies of Majorana bound states in semiconducting nanowires frequently
neglect the orbital effect of magnetic field. Systematically studying its role
leads us to several conclusions for designing Majoranas in this system.
Specifically, we show that for experimentally relevant parameter values orbital
effect of magnetic field has a stronger impact on the dispersion relation than
the Zeeman effect. While Majoranas do not require a presence of only one
dispersion subband, we observe that the size of the Majoranas becomes
unpractically large, and the band gap unpractically small when more than one
subband is filled. Since the orbital effect of magnetic field breaks several
symmetries of the Hamiltonian, it leads to the appearance of large regions in
parameter space with no band gap whenever the magnetic field is not aligned
with the wire axis. The reflection symmetry of the Hamiltonian with respect to
the plane perpendicular to the wire axis guarantees that the wire stays gapped
in the topologically nontrivial region as long as the field is aligned with the
wire.Comment: 5 pages, 6 figures, data available at
http://dx.doi.org/10.4121/uuid:20f1c784-1143-4c61-a03d-7a3454914ab
Robustness of edge states in graphene quantum dots
We analyze the single particle states at the edges of disordered graphene
quantum dots. We show that generic graphene quantum dots support a number of
edge states proportional to circumference of the dot over the lattice constant.
Our analytical theory agrees well with numerical simulations. Perturbations
breaking electron-hole symmetry like next-nearest neighbor hopping or edge
impurities shift the edge states away from zero energy but do not change their
total amount. We discuss the possibility of detecting the edge states in an
antidot array and provide an upper bound on the magnetic moment of a graphene
dot.Comment: Added figure 6, extended discussion (version as accepted by Physical
Review B
Detection of valley polarization in graphene by a superconducting contact
Because the valleys in the band structure of graphene are related by
time-reversal symmetry, electrons from one valley are reflected as holes from
the other valley at the junction with a superconductor. We show how this
Andreev reflection can be used to detect the valley polarization of edge states
produced by a magnetic field. In the absence of intervalley relaxation, the
conductance G_NS=2(e^2/h)(1-cos(Theta)) of the junction on the lowest quantum
Hall plateau is entirely determined by the angle Theta between the valley
isospins of the edge states approaching and leaving the superconductor. If the
superconductor covers a single edge, Theta=0 and no current can enter the
superconductor. A measurement of G_NS then determines the intervalley
relaxation time.Comment: 4 pages, 4 figure
Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
We show how the superconducting phase difference in a Josephson junction may
be used to split the Kramers degeneracy of its energy levels and to remove all
the properties associated with time reversal symmetry. The superconducting
phase difference is known to be ineffective in two-terminal short Josephson
junctions, where irrespective of the junction structure the induced Kramers
degeneracy splitting is suppressed and the ground state fermion parity must
stay even, so that a protected zero-energy Andreev level crossing may never
appear. Our main result is that these limitations can be completely avoided by
using multi-terminal Josephson junctions. There the Kramers degeneracy breaking
becomes comparable to the superconducting gap, and applying phase differences
may cause the change of the ground state fermion parity from even to odd. We
prove that the necessary condition for the appearance of a fermion parity
switch is the presence of a "discrete vortex" in the junction: the situation
when the phases of the superconducting leads wind by . Our approach
offers new strategies for creation of Majorana bound states as well as spin
manipulation. Our proposal can be implemented using any low density, high
spin-orbit material such as InAs quantum wells, and can be detected using
standard tools.Comment: Source code available as ancillary files. 10 pages, 7 figures. v2:
minor changes, published versio
Majorana-based fermionic quantum computation
Because Majorana zero modes store quantum information non-locally, they are
protected from noise, and have been proposed as a building block for a quantum
computer. We show how to use the same protection from noise to implement
universal fermionic quantum computation. Our architecture requires only two
Majoranas to encode a fermionic quantum degree of freedom, compared to
alternative implementations which require a minimum of four Majoranas for a
spin quantum degree of freedom. The fermionic degrees of freedom support both
unitary coupled cluster variational quantum eigensolver and quantum phase
estimation algorithms, proposed for quantum chemistry simulations. Because we
avoid the Jordan-Wigner transformation, our scheme has a lower overhead for
implementing both of these algorithms, and the simulation of Trotterized
Hubbard Hamiltonian in time per unitary step. We finally
demonstrate magic state distillation in our fermionic architecture, giving a
universal set of topologically protected fermionic quantum gates.Comment: 4 pages + 4 page appendix, 4 figures, 2 table
Probing Neutral Majorana Fermion Edge Modes with Charge Transport
We propose two experiments to probe the Majorana fermion edge states that
occur at a junction between a superconductor and a magnet deposited on the
surface of a topological insulator. Combining two Majorana fermions into a
single Dirac fermion on a magnetic domain wall allows the neutral Majorana
fermions to be probed with charge transport. We will discuss a novel
interferometer for Majorana fermions, which probes their Z_2 phase. This setup
also allows the transmission of neutral Majorana fermions through a point
contact to be measured. We introduce a point contact formed by a
superconducting junction and show that its transmission can be controlled by
the phase difference across the junction. We discuss the feasibility of these
experiments using the recently discovered topological insulator Bi_2 Se_3.Comment: 4 page
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