| Title: |
Universal Adapters between Quantum Low-Density Parity Check Codes |
| Authors: |
Esha Swaroop; Tomas Jochym-O'Connor; Theodore J. Yoder |
| Source: |
PRX Quantum, Vol 7, Iss 1, p 010324 (2026) |
| Publisher Information: |
American Physical Society |
| Publication Year: |
2026 |
| Collection: |
Directory of Open Access Journals: DOAJ Articles |
| Subject Terms: |
Physics; QC1-999; Computer software; QA76.75-76.765 |
| Description: |
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 O[over ~](td) additional qubits and checks, up to a factor polylogarithmic in d. As a special case, for some geometrically local codes in fixed D≥2 dimensions, only O(td) additional qubits and checks are required instead. By extending the adapter in the case t=2, we also construct a toric code adapter that uses O(d^{2}) additional qubits and checks to perform addressable logical cnot gates on arbitrary LDPC codes via Dehn twists. To obtain these results, we develop a more general form of graph edge expansion and the SkipTree algorithm, which ensures a sparse transformation between different weight-2 check bases for the classical repetition code. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
https://doi.org/10.1103/1g44-jp62; https://doaj.org/toc/2691-3399; https://doaj.org/article/651f066d33b74f4ba1cb60f35d406082 |
| DOI: |
10.1103/1g44-jp62 |
| Availability: |
https://doi.org/10.1103/1g44-jp62; https://doaj.org/article/651f066d33b74f4ba1cb60f35d406082 |
| Accession Number: |
edsbas.6E89683 |
| Database: |
BASE |