Universal adapters between quantum LDPC codes: graph-based constructions

We propose the repetition code adapter as a novel method to perform joint logical Pauli measurement within a quantum low-density parity check (LDPC) codeblock or between separate such codeblocks. This adapter is universal in the sense that it works regardless of the LDPC codes involved and the Paulis being measured. Since logical Pauli measurements offer a route to universal quantum computation provided magic states are available, our repetition code adapter is a flexible tool to compute fault-tolerantly with arbitrary LDPC codes.

This talk will expand upon a classical algorithm, the SkipTree algorithm, that is of use for sparsely transforming the original parity code checks into ones that are of use for a repetition code adapter. We also further comment on the use of these adapters in geometrically-local codes and expand upon savings and constructions in this setting.