If qubits only talk to 1D neighbors, is constant rate fault tolerance possible? Last year I referee'd a paper claiming it wasn't. My review was "this is wrong but the constructive disproof is too large for this review". Clearly a reviewer 2 move. Sorry. But I was right! scirate.com/arxiv/2502.1... - ThreadSky

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craiggidney.bsky.social • 5 days ago

If qubits only talk to 1D neighbors, is constant rate fault tolerance possible?

Last year I referee'd a paper claiming it wasn't. My review was "this is wrong but the constructive disproof is too large for this review".

Clearly a reviewer 2 move. Sorry. But I was right! https://scirate.com/arxiv/2502.16132

Comments

dripto.bsky.social•5 days ago

Would have lower overhead if it was 2D

craiggidney.bsky.social•5 days ago

Shambles

craiggidney.bsky.social•5 days ago

The overarching idea is simple: concatenate ever-larger Hamming codes (for constant rate) and measure stabilizers using Shor's cat trick (for fault tolerance).

The details are annoying, but the result is a 1D fault tolerant quantum computer with constant spatial overhead.

craiggidney.bsky.social•5 days ago

To be clear, you'd never actually use this. The time overheads are awful, and even a single permanently broken qubit would partition the computer. Maybe it leads to other ideas that lead to other ideas that lead to something useful... for now it was just for fun.

craiggidney.bsky.social•5 days ago

Thiago put together a nice plot summarizing how this result fits into other results about bounds of time/space overhead vs locality. In terms of this plot, the paper's goal was to put a circle in the O(1) column, but not in the "all" row.

sejaques.bsky.social•4 days ago

"Acknowledgements: We'd like to thank the authors of [insert manuscript here] for being so wrong that we were driven to do this research out of spite"

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