8,359 research outputs found
Classification of topologically protected gates for local stabilizer codes
Given a quantum error correcting code, an important task is to find encoded
operations that can be implemented efficiently and fault-tolerantly. In this
Letter we focus on topological stabilizer codes and encoded unitary gates that
can be implemented by a constant-depth quantum circuit. Such gates have a
certain degree of protection since propagation of errors in a constant-depth
circuit is limited by a constant size light cone. For the 2D geometry we show
that constant-depth circuits can only implement a finite group of encoded gates
known as the Clifford group. This implies that topological protection must be
"turned off" for at least some steps in the computation in order to achieve
universality. For the 3D geometry we show that an encoded gate U is
implementable by a constant-depth circuit only if the image of any Pauli
operator under conjugation by U belongs to the Clifford group. This class of
gates includes some non-Clifford gates such as the \pi/8 rotation. Our
classification applies to any stabilizer code with geometrically local
stabilizers and sufficiently large code distance.Comment: 6 pages, 2 figure
Topological insulator and the Dirac equation
We present a general description of topological insulators from the point of
view of Dirac equations. The Z_{2} index for the Dirac equation is always zero,
and thus the Dirac equation is topologically trivial. After the quadratic B
term in momentum is introduced to correct the mass term m or the band gap of
the Dirac equation, the Z_{2} index is modified as 1 for mB>0 and 0 for mB<0.
For a fixed B there exists a topological quantum phase transition from a
topologically trivial system to a non-trivial one system when the sign of mass
m changes. A series of solutions near the boundary in the modified Dirac
equation are obtained, which is characteristic of topological insulator. From
the solutions of the bound states and the Z_{2} index we establish a relation
between the Dirac equation and topological insulators.Comment: 9 pages, published versio
Isospin Dependence of the Spin-Orbit Force and Effective Nuclear Potentials,
The isospin dependence of the spin-orbit potential is investigated for an
effective Skyrme-like energy functional suitable for density dependent
Hartree-Fock calculations. The magnitude of the isospin dependence is obtained
from a fit to experimental data on finite spherical nuclei. It is found to be
close to that of relativistic Hartree models. Consequently, the anomalous kink
in the isotope shifts of Pb nuclei is well reproduced.Comment: Revised, 11 pages (Revtex) and 2 figures available upon request,
Preprint MPA-833, Physical Review Letters (in press)
The classical capacity of quantum thermal noise channels to within 1.45 bits
We find a tight upper bound for the classical capacity of quantum thermal
noise channels that is within bits of Holevo's lower bound. This
lower bound is achievable using unentangled, classical signal states, namely
displaced coherent states. Thus, we find that while quantum tricks might offer
benefits, when it comes to classical communication they can only help a bit.Comment: Two pages plus a bi
Resonant Tunneling through Multi-Level and Double Quantum Dots
We study resonant tunneling through quantum-dot systems in the presence of
strong Coulomb repulsion and coupling to the metallic leads. Motivated by
recent experiments we concentrate on (i) a single dot with two energy levels
and (ii) a double dot with one level in each dot. Each level is twofold
spin-degenerate. Depending on the level spacing these systems are physical
realizations of different Kondo-type models. Using a real-time diagrammatic
formulation we evaluate the spectral density and the non-linear conductance.
The latter shows a novel triple-peak resonant structure.Comment: 4 pages, ReVTeX, 4 Postscript figure
Towards the specification and verification of modal properties for structured systems
System specification formalisms should come with suitable property specification languages and effective verification tools. We sketch a framework for the verification of quantified temporal properties of systems with dynamically evolving structure. We consider visual specification formalisms like graph transformation systems (GTS) where program states are modelled as graphs, and the program
behavior is specified by graph transformation rules. The state space of a GTS can be represented as a graph transition system (GTrS), i.e. a transition system with states and transitions labelled, respectively, with a graph, and with a partial morphism representing the evolution of state components. Unfortunately, GTrSs are prohibitively large or infinite even for simple systems, making verification intractable and hence calling for appropriate abstraction techniques
Contribution of Scalar Loops to the Three-Photon Decay of the Z
I corrected 3 mistakes from the first version: that were an omitted Feynman
integration in the function f^3_{ij}, a factor of 2 in front of log f^3_{ij} in
eq.2 and an overall factor of 2 in Fig.1 c). The final result is changed
drastically. Doing an expansion in the Higgs mass I show that the matrix
element is identically 0 in the order (MZ/MH)^2, which is due to gauge
invariance. Left with an amplitude of the order (MZ/MH)^4 the final result is
that the scalar contribution to this decay rate is several orders of magnitude
smaller than those of the W boson and fermions.Comment: 6 pages, plain Tex, 1 figure available under request via fax or mail,
OCIP/C-93-5, UQAM-PHE-93/0
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