Universal adapters between quantum LDPC codes

Understand

We propose the repetition code adapter as a way to perform joint logical Pauli measurements within a quantum low-density parity check (LDPC) codeblock or between separate such codeblocks, thus providing a flexible tool for fault-tolerant computation with quantum LDPC codes.

• This adapter is universal in the sense that it works regardless of the LDPC codes involved and the logical Paulis being measured.
• The construction achieves joint logical Pauli measurement of $t$ weight $O(d)$ operators using $O(d)$ time and $\tilde O(td)$ additional qubits and checks, up to a factor polylogarithmic in $d$.
• As a special case, for some geometrically-local codes in fixed $D\ge2$ dimensions, only $O(td)$ additional qubits and checks are required instead.