373 research outputs found
Kitaev spin models from topological nanowire networks
We show that networks of topological nanowires can realize the physics of
exactly solvable Kitaev spin models with two-body interactions. This connection
arises from the description of the low-energy theory of both systems in terms
of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana
description provides a convenient representation to solve the model, whereas in
an array of topological nanowires it arises, because the physical Majorana
modes localized at wire ends permit tunnelling between wire ends and across
different Josephson junctions. We explicitly show that an array of junctions of
three wires -- a setup relevant to topological quantum computing with nanowires
-- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a
decorated honeycomb lattice. Translating the results from the latter, we show
that the network can be constructed to give rise to collective states
characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an
array can be associated with vortex-like quasi-particle excitations. Finally,
we analyze the stability of the collective states as well as that of the
network as a quantum information processor. We show that decoherence inducing
instabilities, be them due to disorder or phase fluctuations, can be understood
in terms of proliferation of the vortex-like quasi-particles.Comment: 15 pages, 9 figure
Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control
We derive expressions for the invariant length element and measure for the
simple compact Lie group SU(4) in a coordinate system particularly suitable for
treating entanglement in quantum information processing. Using this metric, we
compute the invariant volume of the space of two-qubit perfect entanglers. We
find that this volume corresponds to more than 84% of the total invariant
volume of the space of two-qubit gates. This same metric is also used to
determine the effective target sizes that selected gates will present in any
quantum-control procedure designed to implement them.Comment: 27 pages, 5 figure
Graphical Calculus for the Double Affine Q-Dependent Braid Group
We define a double affine -dependent braid group. This group is
constructed by appending to the braid group a set of operators , before
extending it to an affine -dependent braid group. We show specifically that
the elliptic braid group and the double affine Hecke algebra (DAHA) can be
obtained as quotient groups. Complementing this we present a pictorial
representation of the double affine -dependent braid group based on ribbons
living in a toroid. We show that in this pictorial representation we can fully
describe any DAHA. Specifically, we graphically describe the parameter upon
which this algebra is dependent and show that in this particular representation
corresponds to a twist in the ribbon
Implementation of a Stochastic Optical Quantum Circuit Simulator ( SOQCS )
We present Stochastic Optical Quantum Circuit Simulator (SOQCS) C++/Python
library for the simulation of quantum optical circuits, and we provide its
implementation details. SOQCS offers a framework to define, simulate and study
quantum linear optical circuits in the presence of various imperfections. These
come from partial distinguishability of photons, lossy propagation media,
unbalanced beamsplitters and non-ideal emitters and detectors for example.
SOQCS is developed as a series of different modules which provide quantum
circuits, different simulator cores and tools to analyze the output. Quantum
circuits can be defined from basic components, including emitters, linear
optical elements, delays and detectors. Post-selection can be configured
straightforwardly as part of detector definitions. An important attribute of
SOQCS is its modularity which allows for its further development in the future.Comment: 25 pages, 10 figure
Implementation of photon partial distinguishability in a quantum optical circuit simulation
We are concerned with numerical simulations of quantum optical circuits under
certain realistic conditions, specifically that photon quantum states are not
perfectly indistinguishable. The partial photon distinguishability presents a
serious limitation in implementation of optical quantum information processing.
In order to properly assess its effect on quantum information protocols,
accurate numerical simulations, which closely emulate quantum circuit
operations, are essential. Our specific objective is to provide a computer
implementation of the partial photon distinguishability which is in principle
applicable to existing simulation techniques used for ideal quantum circuits
and which avoids a need for their significant modification. Our approach is
based on the Gram-Schmidt orthonormalization process, which is well suited for
our purpose. Photonic quantum states are represented by wavepackets which
contain information on their time and frequency distributions. In order to
account for the partial photon distinguishability, we expand the number of
degrees of freedom associated with the circuit operation extending the
definition of the photon channels to incorporate wavepacket degrees of freedom.
This strategy allows to define delay operations in the same footing as the
linear optical elements.Comment: 11 pages, 5 figure
Zero energy and chiral edge modes in a p-wave magnetic spin model
In this work we discuss the formation of zero energy vortex and chiral edge modes in a fermionic representation
of the Kitaev honeycomb model. We introduce the representation and show how the associated
Jordan-Wigner procedure naturally defines the so-called branch cuts that connect the topological vortex excitations.
Using this notion of the branch cuts we show how to, in the non-Abelian phase of the model, describe
the Majorana zero mode structure associated with vortex excitations. Furthermore we show how, by intersecting
the edges between Abelian and non-Abelian domains, the branch cuts dictate the character of the chiral
edge modes. In particular we will see in what situations the exact zero energy Majorana edge modes exist. On
a cylinder, and for the particular instances where the Abelian phase of the model is the full vacuum, we have
been able to exactly solve for the systems edge energy eigensolutions and derive a recursive formula that
exactly describes the edge mode structure. Penetration depth is also calculated and shown to be dependent on
the momentum of the edge mode. These solutions also describe the overall character of the fully open non-
Abelian domain and are excellent approximations at moderate distances from the corners
Examining coupled-channel effects in radiative charmonium transitions
Coupled-channel effects due to coupling of charmonia to the charmed and
anticharmed mesons are of current interest in heavy quarkonium physics.
However, the effects have not been unambiguously established. In this paper, a
clean method is proposed in order to examine the coupled-channel effects in
charmonium transitions. We show that the hindered M1 radiative transitions from
the 2P to 1P charmonia are suitable for this purpose. We suggest to measure one
or more of the ratios Gamma(h_c'-->chi_{cJ} gamma)/Gamma(chi_{cJ}'-->chi_{cJ}
pi^0) and Gamma(chi_{cJ}'-->h_c gamma)/Gamma(chi_{cJ}'-->chi_{cJ} pi^0), for
which highly nontrivial and parameter-free predictions are given. The picture
can also be tested using both unquenched and quenched lattice calculations.Comment: 5 pages, 2 figures. Numerical results corrected. Accepted for
publication in Phys. Rev. Let
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