I'm releasing a series of videos called "Quantum Computer Programming in 100 Easy Lessons".
https://t.co/lfKXwEIHWU
It will cover the 'usual' content (...CHSH, Grover, Factoring), but with some expositional innovations that I *hope* will make it easier for beginners.
Happy to share that our better-than-2 approximation results for k-median are now on arXiv:
https://t.co/NvjU9FQfHh
https://t.co/6lPuN5Voyc
It has been a pleasure working with this fantastic group: @rares_buhai , Vincent Cohen-Addad, Henry Fleischmann, @anupamg , Antoni "Toni" Jubés Monforte, Madhusudhan Reddy Pittu, @mstou73, and @LukasBirdyy
A special shout-out to Toni, who started working on this problem for his Master's thesis almost two years ago. His work led to the impressive analysis of the factor-revealing LP!
Now on to other things...
I looked forward to this cleanup! Nikloai Chukhin (https://t.co/zYQ8ZIAUc4) significantly cleans and extends the OpenAI 2^(ω(sqrt(n))) lower bound for depth-3 circuits:
The (4n-1)-bit function sum_ij a_{i+j}x_iy_j mod 2 needs depth-d circuits of size 2^(Ω~(n log n)^{1/(d-1)}).
@TCzajka Yeah, I just have no intuition about whether the algorithm can be made oblivious. But if you think it seems likely... that would be cool. Hopefully someone will work it out. Because this result seems noticeably more compelling to me if it also works for circuits.
An amazing result in online algorithms. I worked on this for over a decade and it is fantastic to see a solution that looks very clean! Also great to see an expert behind the wheels. Congratulations @sahilsingla81 https://t.co/zxV6upQoNP
@henryquantum ... one might strive further to get the best of both worlds: "Rich" 2-to-1 with perfect completeness (https://t.co/v4o7gGvgg0). That would imply both results. Perhaps the rumors might concern this?
@henryquantum I guess this result is morally close to 2-to-1 Conjecture with perfect completeness. (Maybe with tweaking you can get 4->2, who knows.)
Then it's true that UGC is somewhat different, being stronger in one sense (1-to-1) and weaker in another (imperfect completeness).
But...