Google's recent announcement of quantum computational supremacy was
exciting from various physics and engineering standpoints, but what
about math? In this talk, I'll explain the probability distributions
over \(\{0,1\}^{53}\) from which Google extracted samples, and what we
know about those distributions' statistical properties. As we'll see,
this topic ties together everything from Archimedes' hat-box theorem
of ~200BC, to the fact that amplitudes in quantum mechanics are over
\(\mathbb{C}\) rather than \(\mathbb{R}\). And it has implications for
questions of such obvious relevance as: how do you verify, using a
classical computer, that Google did its experiment correctly? And how
confident can we be, in the present state of theoretical computer
science, that the task Google perform really is classically hard?
Based in part on joint work with Lijie Chen, Sam Gunn, and others.
1:30-2:30: introductory lecture for
students
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