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Date | Presenter | Topic (hover for abstract) | Links |
---|---|---|---|
January 20 | Louis Golowich |
Quantum local testability of the hemicubic code
Quantum locally testable codes provide a means for
encoding quantum data that protects against errors in
such a way that the errors can be detected using only
local tests on the encoded data. This notion of quantum
local testability (for a certain class of codes, namely
CSS codes) can be expressed as a form of
high-dimensional expansion, which generalizes graph
expansion to chain complexes. We will describe the
state-of-the-art construction of such codes, which is
based on the hemicube, a cellular complex that is
topologically equivalent to the real projective plane.
No prior background in quantum codes will be assumed.
|
arxiv |
January 27 | Louis Golowich |
Recent work and open questions on quantum locally
testable codes
In a continuation of last week's talk, we will first
finish the analysis of the hemicubic code. While the
length-N hemicubic code has order sort(N) distance and
1/log(N) soundness, making it essentially the
state-of-the-art quantum locally testable code, it
remains an open question to improve these parameters to
linear distance and constant soundness (as well as to
improve the rate and locality parameters). We will
discuss this open problem in more depth, and describe
some recent constructions that improve certain
parameters at the cost of others
|
arxiv |
February 3 | Zack Stier |
A quantum algorithm for functions of multiple commuting
Hermitian matrices
We will introduce the multivariate quantum eigenvalue
transform, and discuss an application to matrix
functions of normal matrices. Joint work with
Yonah Borns-Weil
and
Tahsin Saffat.
|