New paper, on lower-depth local encoding circuits for the surface code!

As part of my cultivation paper, I needed to expand the surface code unitarily. Turns out, the circuit I designed generalizes to an injection circuit with half the depth of the previous best circuit!

Paper out today: Cultivating T states directly on the surface code with only 2-qubit gates! Cultivation was first proposed for color codes, but surface codes are easier to work with. In my paper, I develop a scheme for surface code cultivation using a small code deformation.

Our dynamic circuit:
* Has an increased threshold compared to the standard circuit (.29% vs .21%) ✅
* Automatically removes leakage, because every data qubit is measured after every four gates ✅
* Has a teraquop footprint nearly 3x smaller than the standard circuit ✅

However, something interesting happens for the case of the Floquet code: we CAN measure all the two-qubit operators in a layer simultaneously, because they don't overlap! This suggests that dynamic circuits might be uniquely suited for the Floquet code.

However, there is another method for measuring operators without using ancilla qubits, "dynamic" or "morphing" circuits (arXiv:2302.02192). We apply a unitary to the data qubits to shrink a stabilizer to a single-qubit operator, then measure that qubit. E.g., in the surface code:

New paper out, introducing a "dynamic" or "morphing" circuit for implementing the honeycomb Floquet code.

scirate.com/arxiv/2507.0...