Fault-tolerant logical gates on LDPC codes
We show how to measure logical operators on arbitrary LDPC codes by appending additional ancilla qubits. Our scheme significantly improves overhead of prior work by Cohen et al. (Sci. Adv. 8, eabn1717). We give explicit measurement protocols and prove their fault distance. We then apply these techniques to show how to perform all logical Clifford gates on the Gross code. The scheme adds about 100 ancilla qubits to the connectivity graph. This improves over prior work which required 1380 additional ancillas. We demonstrate the practicality of our scheme through circuit-level noise simulations, leveraging a modular decoder that combines BPOSD with matching.