Some cool related works
scirate.com/arxiv/2410.1...
scirate.com/arxiv/2510.0...
scirate.com/arxiv/2510.0...

Thanks again to the quantum surgeons, Alex, Sunny, and Ted!

Finally, we introduce a general upper bound on the fault tolerance of any logical measurement scheme in terms of the spacetime region of the code that is addressed by the measurement procedure.

Our results point to a tradeoff between overhead and addressability for fault-tolerant quantum logic.

We demonstrate an equivalence between block reading and homomorphic measurement, and characterize when this equivalence can preserve fault tolerance.

In the extreme limit of measuring a single logical operator, this scheme reduces to regular lattice surgery with a time overhead that scales with the code distance.

We go on to study partial block reading We characterize the space and time overhead depending on the properties of the subcode being measured.

Here is what block reading looks like on a pair of surface codes.

Block reading is a simple class of hypergraph surgeries that measure transversal logical operators. These measure logicals across copies of a code block in parallel, in constant time and linear qubit overhead. This doesn’t require the code to be single-shot, similar to algorithmic fault tolerance.

This was also fun to listen to.

Quantum low density parity check!

Also see related work with similar results plus a bunch of other cool stuff about random input Layer Codes arxiv.org/abs/2510.06659

Applying this decoder to a family of Layer Codes reveals a strong form of partial self-correction where a growing number of encoded qubits are protected for an exponentially long time in the linear system size, up to a scale that is exponential in the inverse temperature.

& here is the correction:

The concatenated matching decoder involves rounds of minimum-weight perfect-matching on coupled surface code layers, combined with a decoder for an input Quantum Tanner Code.

Layer codes may not be self-correcting in the strict sense but that isn’t the end of the story. Stay tuned!