Extractors: QLDPC Architectures for Efficient Pauli-Based Computation

Understand

In pursuit of large-scale fault-tolerant quantum computation, quantum low-density parity-check (LDPC) codes have been established as promising candidates for low-overhead memory when compared to conventional approaches based on surface codes.

• Performing fault-tolerant logical computation on QLDPC memory, however, has been a long standing challenge in theory and in practice.
• In this work, we propose a new primitive, which we call an $\textit{extractor system}$, that can augment any QLDPC memory into a computational block well-suited for Pauli-based computation.
• In particular, any logical Pauli operator supported on the memory can be fault-tolerantly measured in one logical cycle, consisting of $O(d)$ physical syndrome measurement cycles, without rearranging qubit connectivity.