Code Deformation
Code deformation changes a code's stabilizer group over time to move, grow, shrink, or reshape logical qubits while keeping them protected.
Changing the code in place
Code deformation is the general technique of altering which stabilizers are measured from one round to the next, so that the encoded logical qubits are transformed in a controlled way. By switching checks on and off at the boundary of a region, one can move a logical qubit across the chip, enlarge a patch to increase its distance, shrink it, or split one patch into two. The information stays protected throughout because at every step some code is being enforced.
How it stays safe
When a stabilizer is turned off and a different one turned on, the new stabilizer's value is random until measured, but the measurement outcomes record a Pauli frame that the decoder tracks. As long as the deformation is done gradually, over enough rounds to catch errors, and the intermediate codes retain sufficient distance, the logical information survives. Deformation is essentially a smooth path through the space of stabilizer codes.
- Turn stabilizers on and off to reshape the code over time.
- Move, grow, shrink, merge, or split logical qubits.
- Measurement outcomes define a Pauli frame the decoder follows.
- Intermediate codes must keep enough distance to stay protected.
Uses
Lattice surgery is the most important example: merging and splitting patches are code deformations that implement logical gates. Growing a patch to a larger distance before a critical operation, then shrinking it after, is another. Deformation also underlies the older defect-braiding approach and is used to inject magic states into a computation from a distillation factory.
Conceptually, code deformation reframes computation itself as a sequence of changes to the stabilizer group, rather than as gates applied to fixed logical qubits. This viewpoint, natural for topological codes such as the surface code and color codes, is how most surface-code architectures describe both storage and logic in one unified language.