I thank you for your effort! I am currently missing a lot of the mathematical background necessary to make that post make sense, but I will revisit it if I find myself with the motivation to learn!
Optimization Process
Karma: 614
This is a good point! I’ll send you $20 if you send me your PayPal/Venmo/ETH/??? handle. (In my flailings, I’d stumbled upon this “fractional step” business, but I don’t think I thought about it as hard as it deserved.)
How are you defining “basically equivalent”
Nyeeeh, unfortunately, sort of “I know it when I see it.” It’s kinda neat being able to take a fractional step of a classical elementary CA, but I’m dissatisfied because… ah, because the long-run behavior of the fractional-step operator is basically indistinguishable from the long-run behavior of the corresponding classical CA.
So, tentative operationalization of “basically equivalent”: is “basically equivalent” to a classical elementary CA if the long-run behavior of is very close to the long-run behavior of some , i.e., uh,
...but I can already think of at least one flaw in this operationalization, so, uh, I’m not sure. (Sorry! This being so fuzzy in my head is why I’m asking for help!)
I was imagining the tape wraps around! (And hoping that whatever results fell out would port straightforwardly to infinite tapes.)
I’ve never been familiar enough with group-theory stuff to memorize the names (which, warning, also might mean that it will take you a lot of time to write a sufficiently-dumbed-down version), but the internet suggests is related to… the Minkowski metric? I would be flabbergasted to learn that something so specific-to-our-universe was relevant to this toy mathematical contraption.
I think compared to the literature you’re using an overly restrictive and nonstandard definition of quantum cellular automata.
That makes sense! I’m searching for the simplest cellular-automaton-like thing that’s still interesting to study. I may have gone too far in the “simple” direction; but I’d like to understand why this highly-restricted subset of QCAs is too simple.
Specifically, it only makes sense to me to write as a product of operators like you have if all of the terms are on spatially disjoint regions.
Hmm! That’s not obvious to me; if there’s some general insight like “no operator containing two ~‘partially overlapping’ terms like can be unitary,” I’d happily pay for that!
[Question] Why are there no interesting (1D, 2-state) quantum cellular automata?
If I ran the zoo
Two children’s stories
Things have coalesced near the amphitheater. When the music kicks off again, we’ll go northeast to… approximately here. 47.6309473, −122.3165802 JMJM+99F Seattle, Washington
Announcement 1: I, the organizer, will be 5-10min late. Announcement 2: apparently there’s some music thing happening at the amphitheater! I’ll set up somewhere northeast of the amphitheater when I get there, and post more precise coordinates when I have.
$10 bounty for anybody coming / passing through Capitol Hill: pick up a blind would-be attendee outside the Zeek’s Pizza by 19th and Mercer. DM me your contact information, and I’ll put you in touch, and I’ll pay you on your joint arrival.
Update: the library is unexpectedly closed due to staffing issues. The event is now at Fuel Coffee, one block south and across the street.
Seattle ACX Meetup—Summer 2023
Book Club: Thomas Schelling’s “The Strategy of Conflict”
If the chance of rain is dissuading you: fear not, there’s a newly constructed roof over the amphitheater!
Hey, folks! PSA: looks like there’s a 50% chance of rain today. Plan A is for it to not rain; plan B is to meet in the rain.
See you soon, I hope!
I have an Anki deck in which I’ve half-heartedly accumulated important quantities. Here are mine! (I keep them all as log10(value in kilogram/meter/second/dollar/whatever seems natural), to make multiplication easy.)