Code Deformation and Braiding
Reshaping a code's stabilizers over time moves logical qubits and braids defects, implementing gates as spacetime operations on the lattice.
Changing the code as you go
Code deformation means turning some stabilizers off and others on over successive rounds, gradually reshaping the region of the lattice that carries a logical qubit. Because the change is made by measuring new stabilizers rather than by decoding, the information stays protected throughout. Grown, shrunk, and moved patches let logical qubits travel and interact.
Braiding defects
One classic form uses defects, holes punched in the code by not measuring certain stabilizers. Each pair of holes encodes a logical qubit. Dragging one hole around another traces a braid in spacetime, and the topology of that braid determines the logical operation, in the surface code a logical CNOT. The result depends only on the braid's topology, giving geometric robustness.
- Deformation switches stabilizer sets round by round, never decoding.
- Defects (holes) encode logical qubits whose braids give gates.
- The operation is a spacetime topological invariant.
- Distance must be maintained throughout the deformation schedule.
Braiding-based surface-code computation was the original blueprint, but lattice surgery has largely replaced it because surgery uses qubits more efficiently for the same operations. Both are instances of the same principle: logical gates as controlled, fault-tolerant changes to which stabilizers are measured over time.
The essential safety condition is that the effective distance never drops during the schedule. A poorly designed deformation could momentarily create a short logical operator through which an error slips. Deformation schedules are therefore designed and verified so that the minimum spacetime distance stays at the target value at every step.