[quantum-info] Next week's PIQuDos
Markus Mueller
mmueller at perimeterinstitute.ca
Fri Oct 26 04:17:41 EDT 2012
Hi all,
next week, we have a talk by Alexey Kovalev on Monday 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
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