this is the real reason why the mayans stopped counting in 2012

If you run with your idea and think about Fourier analysis, then energy being frequency means more energy is like a resource to make more complicated shapes in the time domain.

This is actually a “penny drop” for me thanks. The closest I’d come to understanding energy (besides formal ways like conserved charge of time translation etc) is that it’s the amount of “stuff that can happen” in a physical system.

To be fair, if you look at the wave function in Grover’s algorithm it really does try every combination. It’s just that you have to extract the properties of the state by sampling it, so the rest of the algorithm involves exponentially many rounds of signal boosting to make the sampling succeed.

We also found energy eigenstates for a free particle and the infinite square well. The former are continuous, while the latter are discrete, which is a crucial lesson. QM doesn’t say that Nature is discrete, only that certain observables have a discrete spectrum.

A depressing thing I’ve found is that the left is just in denial about this. I’ve met quite a few people where if I mention Fox News they say “I’ve never watched it”. How will you understand your own country if you don’t from time to time?

Somehow the speed up is both quadratic and exponential

What if Wigner's friend was Schrodinger's cat?

I think there could be other reasons to build quantum computers, if more serious investigations were done into them. Power consumption and time to solution mainly. I think supremacy over classical is mostly a dead end, especially for NISQ.

I should add: not just simulate, but to better accuracy than they have reported. And in a scalable way.

Just to be clear, I don’t think we claimed anywhere that D-Wave has no advantage. We see that as something they still have the burden of proving (if it’s even conceivably provable). We just showed it’s possible to simulate a large range of the same protocols.

Actually we just haven’t tried that one yet … maybe it’s hard, maybe not. It’s an open question.

Maybe the question should be why D-Wave’s was timed to land just before APS :^)

Yeah I can ask my coauthors again but I certainly had no personal idea about the timing. It is pretty wild.

Could perhaps have done it sooner but one of the key methods we used was only invented by a different group last fall. I’ve been emphasizing to journalists that it’s a fast-moving, dynamic field!

In fact, we posted when we did because of APS Physics Summit coming up and the first author wanted to speak on it. The timing with Science’s publication was a coincidence. It’s been surprising to us too.