3,398 research outputs found
On skew tau-functions in higher spin theory
Recent studies of higher spin theory in three dimensions concentrate on
Wilson loops in Chern-Simons theory, which in the classical limit reduce to
peculiar corner matrix elements between the highest and lowest weight states in
a given representation of SL(N). Despite these "skew" tau-functions can seem
very different from conventional ones, which are the matrix elements between
the two highest weight states, they also satisfy the Toda recursion between
different fundamental representations. Moreover, in the most popular examples
they possess simple representations in terms of matrix models and Schur
functions. We provide a brief introduction to this new interesting field,
which, after quantization, can serve as an additional bridge between knot and
integrability theories.Comment: 36 page
Measure of decoherence in quantum error correction for solid-state quantum computing
We considered the interaction of semiconductor quantum register with noisy
environment leading to various types of qubit errors. We analysed both phase
and amplitude decays during the process of electron-phonon interaction. The
performance of quantum error correction codes (QECC) which will be inevitably
used in full scale quantum information processors was studied in realistic
conditions in semiconductor nanostructures. As a hardware basis for quantum bit
we chose the quantum spatial states of single electron in semiconductor coupled
double quantum dot system. The modified 5- and 9-qubit quantum error correction
(QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were
applied to quantum register. 5-qubit error correction procedures were
implemented for Si charge double dot qubits in the presence of acoustic phonon
environment. Chi-matrix, Choi-Jamiolkowski state and measure of decoherence
techniques were used to quantify qubit fault-tolerance. Our results showed that
the introduction of above quantum error correction techniques at small phonon
noise levels provided quadratic improvement of output error rates. The
efficiency of 5-qubits quantum error correction algorithm in semiconductor
quantum information processors was demonstrated
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