I've never thought about the viability of fitting my carry on luggage into a CRJ overhead bin, but I will from now on

Though, it's true that we should be much more mindful of the rate of the outer code in a concatenated scheme

LDPC does reduce the effects of hook errors quite a bit. Noise-biasing the syndrome extraction circuit does help, but it might not be sufficient if a rare large error event (e.g. ionizing radiation) blows up a surface code patch mid-cycle. That said, we don't have any good models of this.

To my understanding, the techniques in this paper (Golowich and Guruswami) use products of higher chain complexes although they require qLTCs arxiv.org/abs/2411.03646

I also want to advertise a recent result by Bergamaschi and Gidney that shows constant space overhead quantum computation can be accomplished with the connectivity of a line (2502.16132). 9/9

These sorts of constructions also have good resilience against rare error bursts as long as they are sufficiently spatially localized, so we may see additional reasons to use them as we understand our error sources better. 8/9

The Yoked Surface codes by Gidney, Newman, Brooks, and Jones (2312.04522) is a related non-asymptotic approach that shows this style of memory has good practical potential. 7/9

We also are interested in making our construction practically relevant and provide a recipe for constructing hierarchical codes / syndrome extraction circuits given an input qLDPC code. This recipe can take advantage of any available long-range connectivity, but it doesn't require it. 6/9

We also saturate (up to log factors) a tradeoff between the volume of syndrome extraction circuits and the desired rate of logical error suppression by Baspin, Fawzi, and Shayeghi (2302.04317). 5/9

To our knowledge, this is the first proof that we can outperform the surface code in the asymptotic regime using purely geometrically local circuits. 4/9

We show that, at a small (log) cost, a quantum memory based on good qLDPC code families can be realized with a threshold using a 2D geometrically local circuit. At the end of the day, we have a memory with rate 1/polylog(N) and error suppression exp(-N/polylog N), exceeding the BPT bound. 3/9

Given known no-go bounds such as the Bravyi-Pouli-Terhal bound, a natural question is whether we can realize the benefits of modern qLDPC code constructions subject to locality constraints. 2/9

Has anyone thought about non-asymptotic bounds on code parameters that include the check weight? Especially near-term it would be useful to know if there's something better out there (or what weight-5, weight-6 checks buys you). I'm happy if it's "solve this crazy LP/SDP."

and I think we can all agree, 0.5" margins are probably not reasonable.

Letting near-failures through risks setting a precedent that people will just ignore the minimum requirements

Can I make the obnoxious suggestion that nix might be the answer?

I think it would be really cool if someone could write a proof of a fault-tolerant threshold theorem in Lean, but it seems like a major uphill battle since it would be from scratch