qLDPC on a String
Break and repair the error-correcting code IonQ ran on a chain of trapped ions in 2026. The BB5 [[18,4,3]] code stores 4 logical qubits in 18 ions, where four distance-3 rotated surface-code patches would take 36. The price is in the picture: every check touches five ions that sit far apart. With all-to-all connectivity that needs no routing. On restricted wiring it costs extra gates: the encoder compiles to 35 two-qubit gates all-to-all and 145 on a heavy-hex layout.
The full app sends the same experiment to a backend as a Qiskit circuit (encode, inject, measure, decode), plots where encoding starts to pay in an idealised noise model, and includes the [[24,4,4]] and [[30,4,5]] codes of the same family.
One round with final readout and a non-fault-tolerant encoder: it demonstrates the code, it does not reproduce IonQ's breakeven result. Polynomials from Table III of arXiv:2606.06455. The surface-code comparison counts data qubits only.