Ryan O'Donnell
@booleananalysis.bsky.social
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Reposted by Ryan O'Donnell
tomvii.bsky.social
Feeling depressed and anxious about the state of the world? Try working on a 375 year-old math problem from the Platonic realm, which should be completely psychologically safe . . .
youtu.be/QH4MviUE0_s
Rupert's Snub Cube and other Math Holes
YouTube video by suckerpinch
youtu.be
Reposted by Ryan O'Donnell
emose.bsky.social
New work with @booleananalysis.bsky.social! We prove instance-optimal bounds for quantum state certification when testers can measure all copies simultaneously, finding that the optimal copy complexity depends on how close to maximally mixed the hypothesis state is.

arxiv.org/abs/2507.06010

1/3
Screenshot of the title and abstract of https://arxiv.org/abs/2507.06010.
booleananalysis.bsky.social
Spread the word: there is a new prize in Theoretical Computer Science in honor of Luca Trevisan--

cs.unibocconi.eu/call-nominat...

(Intent-to-nominate letters due by July 31.)
cs.unibocconi.eu
booleananalysis.bsky.social
J-Live's Braggin' Writes has my top 'thesis' verse, though. ("I displays my credentials over instrumentals...")
booleananalysis.bsky.social
This!

I like to say,

"Let p|A denote distribution p conditioned on event A.

Imagine a world where the laws of probability are the same, except (p|A)|B need not equal (p|B)|A.

Except you don't have to imagine, because it's literally our world!

Now explore probabilistic algorithms in this world."
booleananalysis.bsky.social
There's a reason I called it Quantum Computer Programming in 100 Easy Lessons.
booleananalysis.bsky.social
Meming aside, this looks like a cool paper...
booleananalysis.bsky.social
Sigbovik's looking good this year. Come for the tom7/suckerpinch video preview, stay for Shor vs a random number generator...
craiggidney.bsky.social
For sigbovik, I factored all 8 bit ints (up to 255) with a quantum computer github.com/strilanc/fal...

I did it as legit as I possibly could. I ran a correct circuit with no optimization shenanigans. I did correct pre/postprocessing.

It took 121 quantum samples to finish the entire task.

But...
Reposted by Ryan O'Donnell
anupamg.bsky.social
#STOC2025 (June 23-27, Prague) Theory Fest is looking for workshop proposals. The deadline is March 9th.

Apply here: stoc2025theoryfest.netlify.app
Vite + React + TS
stoc2025theoryfest.netlify.app
Reposted by Ryan O'Donnell
rrwilliams.bsky.social
New paper: Simulating Time With Square-Root Space

people.csail.mit.edu/rrw/time-vs-...

It's still hard for me to believe it myself, but I seem to have shown that TIME[t] is contained in SPACE[sqrt{t log t}].

To appear in STOC. Comments are very welcome!
people.csail.mit.edu
booleananalysis.bsky.social
[...] "x1 += x2" and "x1 += x3". Similarly for "x2 -= x4".

Finally, we posit: Doing "x1 += x2" 256 times in a row is equivalent to doing nothing
(maybe shoulda called it "x1 += x2 mod 256")
and sim. for doing "x2 += x3", "x3 += x4" 256x in a row.

Can you prove "x1 -= x3" commutes with "x2 -= x4"?
booleananalysis.bsky.social
PL puzzle. Say we have instructions called
"x1 += x2", "x2 += x3", "x3 += x4",
and versions with "-=" that cancel them.

We define a program
"x1 += x2"
"x2 += x3"
"x1 -= x2"
"x2 -= x3",
and abbreviate it "x1 -= x3". We similarly define "x2 -= x4".

We posit that "x1 -= x3" commutes with [...]
booleananalysis.bsky.social
Group theory puzzle. We have symbols ♀️,🏁,♂️.
Also define ♕=♀️🏁♀️⁻¹🏁⁻¹ and ♔=♂️🏁♂️⁻¹🏁⁻¹.

We posit:
♀️♕=♕♀️ and 🏁♕=♕🏁 and ♂️♔=♔♂️ and 🏁♔=♔🏁.
And we posit:
♀️²⁰²⁵=🏁²⁰²⁵=♂️²⁰²⁵=1 (identity).

Can you prove ♕♔=♔♕?
booleananalysis.bsky.social
Wow, very cool question!
booleananalysis.bsky.social
... which is to formalize the analogous theorems for the B_3 case (specifically, Sec. 8 of my recent paper with Noah: arxiv.org/pdf/2411.05916).

The proofs there are 70 pages of Noah solving the word problem by hand. So it will be nice to have a computer check his work -- a team is being assembled!
arxiv.org
booleananalysis.bsky.social
Cayden Codel & Noah Singer have formalized in Lean the climactic theorems of the Kaufman-Oppenheim paper that shows the A_3-type coset complex HDXs are cosystolic expanders! (I.e., Sec. 7.2 of arxiv.org/abs/1907.01259)

It's a warmup for the main project...
arxiv.org
booleananalysis.bsky.social
Bravo to 1st-year undergraduate Tyler Yang at CMU, who was the first person to write up and make videos for all* 100 exercises in my "Quantum Computer Programming in 100 Easy Lessons" series! (www.youtube.com/watch?v=XtDJ...)

*more or less all
#1/100: Toggling qubits || Quantum Computer Programming in 100 Easy Lessons
YouTube video by Ryan O'Donnell
www.youtube.com
booleananalysis.bsky.social
Random d-regular graphs are (2-sided) Ramanujan with probability 69%:

arxiv.org/pdf/2412.20263 by Jiaoyang Huang, Theo Mckenzie, HT Yau.

In particular, infinitely many 7-regular Ramanujan graphs exist.
booleananalysis.bsky.social
There's a nice recentish paper that finds the longest increasing subsequence in space O(S) and time O~(n^2/S) provides S is at least sqrt(n). An open question I like: Is there a poly-time algorithm with S=o(sqrt n)?
booleananalysis.bsky.social
This is a great book! If you're not at the beach, keep it at your bedside table for some nighttime reading.