In a celebrated result from the $60$'s, Berlekamp showed that feedback can be used to increase the maximum fraction of adversarial noise that can be tolerated by binary error correcting codes from $1/4$ to $1/3$. However, his result relies on the assumption that feedback is "continuous", i.e., after every utilization ... more >>>

The Forster transform is a method of regularizing a dataset
by placing it in {\em radial isotropic position}
while maintaining some of its essential properties.
Forster transforms have played a key role in a diverse range of settings
spanning computer science and functional analysis. Prior work had given
{\em ... more >>>

We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even sub-constant) fraction of their inputs into ones that are correct on all inputs. This stands ... more >>>