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!
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!
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.
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.)