Overall this article looks pretty good. There was one major numerical error I noticed, but then the article corrected itself at the end. This was the error:
> With an error rate of 1% the surface error correction code requires ~ 500 physical qubits required to encode one logical qubit.
This was the correction near the end:
> With an error rate of 0.3% the surface error correction code requires ~ 10 thousand physical qubits to encode one logical qubit to achieve 10^-10 logical qubit error rate.
The qubit count at an error rate of 1% was clearly off because the threshold of the surface code under circuit noise is a bit below 1%. Meaning at 1% it would have infinite cost; way more than 500. To get good numbers you need be well below the threshold. At a 0.1% error rate, assuming a square grid of qubits with local connections, the best physical-per-logical estimate that I'm aware of is 600, from surface codes plus a few extra parity checks layered on top [1][2]. Another code that achieves a teraquop footprint of ~600 on a planar grid is the honeycomb code [3][4] but that number requires a dissipative two qubit gate which seems to be harder to build than the usual unitary ones.
> With an error rate of 1% the surface error correction code requires ~ 500 physical qubits required to encode one logical qubit.
This was the correction near the end:
> With an error rate of 0.3% the surface error correction code requires ~ 10 thousand physical qubits to encode one logical qubit to achieve 10^-10 logical qubit error rate.
The qubit count at an error rate of 1% was clearly off because the threshold of the surface code under circuit noise is a bit below 1%. Meaning at 1% it would have infinite cost; way more than 500. To get good numbers you need be well below the threshold. At a 0.1% error rate, assuming a square grid of qubits with local connections, the best physical-per-logical estimate that I'm aware of is 600, from surface codes plus a few extra parity checks layered on top [1][2]. Another code that achieves a teraquop footprint of ~600 on a planar grid is the honeycomb code [3][4] but that number requires a dissipative two qubit gate which seems to be harder to build than the usual unitary ones.
[1]: https://www.youtube.com/watch?v=Ge7fEaXjvq4
[2]: https://arxiv.org/pdf/2312.04522
[3]: https://arxiv.org/abs/2107.02194
[4]: https://arxiv.org/abs/2202.11845