Fault-tolerant protocols through spacetime concatenation

Understand

We introduce a framework called spacetime concatenation for fault-tolerant compilation of syndrome extraction circuits of stabilizer codes.

• Spacetime concatenation enables efficient compilation of syndrome extraction circuits into dynamical codes through structured gadget layouts and encoding matrices, facilitating low-weight measurements while preserving logical information.
• Our framework uses conditions that are sufficient for fault-tolerance of the dynamical code, including not measuring logical operators and preserving the spacetime distance.
• We construct explicit examples of dynamical codes using this framework, including the dynamical bivariate bicycle code and a dynamical Haah code, while illustrating their fault-tolerant properties.