Additional group theory functions for error correction (#351)

---------

Co-authored-by: Kenneth Goodenough <[email protected]>
Co-authored-by: Stefan Krastanov <[email protected]>
Co-authored-by: Stefan Krastanov <[email protected]>

Author: 3 people

CHANGELOG.md

@@ -7,6 +7,12 @@
 
 ## v0.9.13 - dev
 
+- New error correction group theory tools:
+    - `canonicalize_noncomm` function to find a generating set with minimal anticommutivity
+    - `SubsystemCodeTableau` data structure to represent the output of `canonicalize_noncomm`
+    - `commutify` function to find a commutative version of a non-commutative set of Paulis with minimal changes
+    - `matroid_parent` to, for set of Paulis that doesn't represent a state, find a version
+    that does.
 - Implementing additional named two-qubit gates: `sSWAPCX, sInvSWAPCX, sCZSWAP, sCXSWAP, sISWAP, sInvISWAP,
     sSQRTZZ, sInvSQRTZZ`
 

docs/src/references.bib

@@ -403,6 +403,31 @@ @inproceedings{brown2013short
   doi = {10.1109/ISIT.2013.6620245}
 }
 
+@article{RevModPhys.87.307,
+  title = {Quantum error correction for quantum memories},
+  author = {Terhal, Barbara M.},
+  journal = {Rev. Mod. Phys.},
+  volume = {87},
+  issue = {2},
+  pages = {307--346},
+  numpages = {40},
+  year = {2015},
+  month = {Apr},
+  publisher = {American Physical Society},
+  doi = {10.1103/RevModPhys.87.307},
+  url = {https://link.aps.org/doi/10.1103/RevModPhys.87.307}
+}
+
+@misc{goodenough2024bipartiteentanglementnoisystabilizer,
+  title={Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes}, 
+  author={Kenneth Goodenough and Aqil Sajjad and Eneet Kaur and Saikat Guha and Don Towsley},
+  year={2024},
+  eprint={2406.02427},
+  archivePrefix={arXiv},
+  primaryClass={quant-ph},
+  url={https://arxiv.org/abs/2406.02427}, 
+}
+
 @article{panteleev2021degenerate,
   title = {Degenerate {{Quantum LDPC Codes With Good Finite Length Performance}}},
   author = {Panteleev, Pavel and Kalachev, Gleb},

src/QuantumClifford.jl

@@ -78,6 +78,7 @@ export
     graphstate, graphstate!, graph_gatesequence, graph_gate,
     # Group theory tools
     groupify, minimal_generating_set, pauligroup, normalizer, centralizer, contractor, delete_columns,
+    canonicalize_noncomm, commutify, matroid_parent, SubsystemCodeTableau,
     # Clipped Gauge
     canonicalize_clip!, bigram, entanglement_entropy,
     # mctrajectories