Hi all,
this is a reminder of Alexey Kovalev's talk today at 4pm in the Time
Room.
Best wishes,
Markus
Title:
Fault tolerance of "bad" quantum low-density parity check codes
Speaker: Alexey Kovalev (University of California)
Abstract:
In my talk, I will discuss various families of quantum
low-density parity check
(LDPC) codes and their fault tolerance. Such codes yield finite
code rates and
at the same time
simplify error correction and encoding due to low-weight
stabilizer
generators. As an example, a large family of
hypergraph-product codes is considered. Of particular interest are
families of
quantum LDPC codes with finite rate and distance scaling as square
root of blocklength since this represents the best known exponent
in
distance scaling, even for codes of dimensionality 1. In relation
to such
codes, we show that any family of LDPC codes, quantum or
classical,
where distance scales as a positive power of the block length, $d
\propto n^\alpha$, $\alpha>0$ ($\alpha<1$ for "bad"
codes), can correct all errors with certainty if the
error rate per qubit is sufficiently small. We specifically
analyze the case of LDPC version of the quantum
hypergraph-product codes recently suggested by Tillich and
Z\'emor. These codes are a
finite-rate generalization of the toric codes, and, for
sufficiently
large quantum computers, offer an advantage over the toric codes.
Date: October 29, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Room