High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory

Understand

We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes.

• The codes are defined using a pair of integers $(r,s)$ and have parameters $[\![2r^2s,2(r-1)^2,\leq2s]\!]$, with numerical studies suggesting average-case distance linear in $s$.
• In simulations of circuit-level noise, we observe comparable error suppression to surface codes of similar distance while using approximately five times fewer physical qubits.
• This is true even when radial codes are decoded using a single-shot approach, which can allow for faster logical clock speeds and reduced decoding complexity.