9,868 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
Progressor: Personalized visual access to programming problems
This paper presents Progressor, a visualization of open student models intended to increase the student's motivation to progress on educational content. The system visualizes not only the user's own model, but also the peers' models. It allows sorting the peers' models using a number of criteria, including the overall progress and the progress on a specific topic. Also, in this paper we present results of a classroom study confirming our hypothesis that by showing a student the peers' models and ranking them by progress it is possible to increase the student's motivation to compete and progress in e-learning systems. © 2011 IEEE
Strong Tunneling in Double-Island Structures
We study the electron transport through a system of two low-capacitance metal
islands connected in series between two electrodes. The work is motivated in
part by experiments on semiconducting double-dots, which show intriguing
effects arising from coherent tunneling of electrons and mixing of the
single-electron states across tunneling barriers. In this article, we show how
coherent tunneling affects metallic systems and leads to a mixing of the
macroscopic charge states across the barriers. We apply a recently formulated
RG approach to examine the linear response of the system with high tunnel
conductances (up to 8e^2/h). In addition we calculate the (second order)
cotunneling contributions to the non-linear conductance. Our main results are
that the peaks in the linear and nonlinear conductance as a function of the
gate voltage are reduced and broadened in an asymmetric way, as well as shifted
in their positions. In the limit where the two islands are coupled weakly to
the electrodes, we compare to theoretical results obtained by Golden and
Halperin and Matveev et al. In the opposite case when the two islands are
coupled more strongly to the leads than to each other, the peaks are found to
shift, in qualitative agreement with the recent prediction of Andrei et al. for
a similar double-dot system which exhibits a phase transition.Comment: 12 page
Tunneling resonances in quantum dots: Coulomb interaction modifies the width
Single-electron tunneling through a zero-dimensional state in an asymmetric
double-barrier resonant-tunneling structure is studied. The broadening of steps
in the -- characteristics is found to strongly depend on the polarity of
the applied bias voltage. Based on a qualitative picture for the
finite-life-time broadening of the quantum dot states and a quantitative
comparison of the experimental data with a non-equilibrium transport theory, we
identify this polarity dependence as a clear signature of Coulomb interaction.Comment: 4 pages, 4 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
A de Finetti representation for finite symmetric quantum states
Consider a symmetric quantum state on an n-fold product space, that is, the
state is invariant under permutations of the n subsystems. We show that,
conditioned on the outcomes of an informationally complete measurement applied
to a number of subsystems, the state in the remaining subsystems is close to
having product form. This immediately generalizes the so-called de Finetti
representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe
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