QMATH researchers publish in JAMS
Quantum Intuition leads to progress on Matrix Multiplication Problem. Now published in the Journal of the American Mathematical Society (JAMS).
How fast can you multiply two n-by-n matrices? Time=n^3 was the standard answer until Strassen’s breakthrough in 1969, which did it in sub-cubic time. To this date, it remains open whether a quadratic time algorithm is possible.
To systematically approach the problem, Strassen cast the problem in the language of tensors (arrays of numbers) and showed that nice functions exist that can tackle the problem. Unfortunately, he only showed that they existed and did not know to construct them.
By viewing tensors as entangled quantum states and using their quantum computing intuition, Matthias Christandl (now leader of Quantum for Life Center), Peter Vrana (then visiting professor at QMATH) and Jeroen Zuiddam (Amsterdam) constructed the first family of such functionals.
The work was presented at STOC, a top computer science conference a few years back, but has now been vetted by the mathematics community and appeared in full length in the Journal of the American Mathematical Society (JAMS).
You can read the article here: Universal points in the asymptotic spectrum of tensors. As a bonus, there is a nice connection to cap-sets and slice rank.