I am pretty optimistic that this number of 7x10^4 (to reach a logical error rate of 10^(-12)) can go down quite a lot with further improvements, and that these codes will be used in practice for cat qubits.
Here, we apply this idea to biased-noise qubits and show that, for sufficiently high noise bias, correcting bit-flips only at the outer-code level is more advantageous than correcting it at the inner-code level, as done by the surface or XZZX codes.
Recently, Refs. arxiv.org/abs/2303.04798 and arxiv.org/abs/2312.04522 have shown that concatenating the surface code with a higher-rate outer code can reduce the overall overhead, while staying with a 2D architecture.
New preprint out with @pshanahan62.bsky.social! We introduce a new error-correcting code for biased-noise qubits. Built from the concatenation of two classical codes, it outperforms the surface and XZZX codes when the noise bias exceeds 7x10^4.
arxiv.org/abs/2601.10786
And for instance, you can also prepare a Cx-Cx-X state (a Hadamard CCZ) by unfolding the [[8,3,2]] 3D color code
The suppression scales in p², which is a bit weak, but maybe larger unfolded codes can push the fidelity further, something to explore!
cc @christophe.vuillot.info
Why does it work? The 15 Reed-Muller is 3D, but if one error type dominates, you only need to measure the weight-4 stabilizers, not the weight-8 ones
The nice part is you can unfold these weight-4 checks in 2D!
And this unfolded code can be also merged with a thin surface code
And even with a noise bias as low as 80, a magic state of the same fidelity can be prepared with 175 qubits in the same amount of time
The key insight is that the noise bias enables you to perform distillation at the physical level rather than at the logical level
Probably the last paper of my PhD! We show that biased-noise qubits can greatly reduce the cost of magic state preparation
With high noise bias, just 53 qubits and ~10 error correction cycles are enough to prepare a magic state with logical error≈1e-7
arxiv.org/abs/2507.12511
Diego presenting his work under the expert eye of Craig Gidney
Summary slide of Diego's results
Two talks of Alice&Bob QEC team in parallel this morning:
@diego-ruiz.bsky.social presented his new results on distillation with biased-noise qubits: with bias=30 he already gets 150x reduction!
I talked about implementing rotor codes
So many fun subjects to work on, join our team we are hiring!🐱
1️⃣ It's surprisingly close to the theory, the suppression of bitflips has never been this strong, the lifetime is multiplied by e^4≈50 for every added photon instead of e^2≈7
2️⃣ The bitflip saturates at the same value as the normal cat, a few minutes (cosmic rays?)
