% The basis of the tableaux algorithm

@inproceedings{gottesman1998heisenberg,
  title={The Heisenberg representation of quantum computers},
  author={Gottesman, Daniel},
  booktitle={International Conference on Group Theoretic Methods in Physics},
  year={1998},
  organization={Citeseer},
  url={https://arxiv.org/abs/quant-ph/9807006}
}

@article{aaronson2004improved,
  title={Improved simulation of stabilizer circuits},
  author={Aaronson, Scott and Gottesman, Daniel},
  journal={Physical Review A},
  volume={70},
  number={5},
  pages={052328},
  year={2004},
  publisher={APS},
  doi={10.1103/PhysRevA.70.052328}
}

% Random Stabilizers

@article{koenig2014efficiently,
  title={How to efficiently select an arbitrary Clifford group element},
  author={Koenig, Robert and Smolin, John A},
  journal={Journal of Mathematical Physics},
  volume={55},
  number={12},
  pages={122202},
  year={2014},
  publisher={AIP Publishing},
  doi={10.1063/1.4903507}
}

@article{bravyi2020hadamard,
  title={Hadamard-free circuits expose the structure of the Clifford group},
  author={Bravyi, Sergey and Maslov, Dmitri},
  journal={IEEE Transactions on Information Theory},
  volume={67},
  number={7},
  pages={4546--4563},
  year={2021},
  publisher={IEEE},
  doi={10.1109/TIT.2021.3081415}
}

@inproceedings{berg2020simple,
  title={A simple method for sampling random Clifford operators},
  author={Van Den Berg, Ewout},
  booktitle={2021 IEEE International Conference on Quantum Computing and Engineering (QCE)},
  pages={54--59},
  year={2021},
  organization={IEEE},
  doi={10.1109/QCE52317.2021.00021}
}

@article{li2019measurement,
  title={Measurement-driven entanglement transition in hybrid quantum circuits},
  author={Li, Yaodong and Chen, Xiao and Fisher, Matthew PA},
  journal={Physical Review B},
  volume={100},
  number={13},
  pages={134306},
  year={2019},
  publisher={APS},
  doi={10.1103/PhysRevB.100.134306}
}

% Canonicalization Methods

@article{garcia2012efficient,
  title={Efficient inner-product algorithm for stabilizer states},
  author={Garcia, Hector J and Markov, Igor L and Cross, Andrew W},
  journal={arXiv preprint arXiv:1210.6646},
  year={2012},
  url={https://arxiv.org/abs/1210.6646}
}

@article{audenaert2005entanglement,
  title={Entanglement on mixed stabilizer states: normal forms and reduction procedures},
  author={Audenaert, Koenraad MR and Plenio, Martin B},
  journal={New Journal of Physics},
  volume={7},
  number={1},
  pages={170},
  year={2005},
  publisher={IOP Publishing},
  doi={10.1088/1367-2630/7/1/170}
}

@phdthesis{gottesman1997stabilizer,
  title={Stabilizer codes and quantum error correction},
  author={Gottesman, Daniel},
  year={1997},
  school={California Institute of Technology},
  publisher={California Institute of Technology},
  url={https://arxiv.org/abs/quant-ph/9705052}
}

@article{gullans2020dynamical,
  title={Dynamical purification phase transition induced by quantum measurements},
  author={Gullans, Michael J and Huse, David A},
  journal={Physical Review X},
  volume={10},
  number={4},
  pages={041020},
  year={2020},
  publisher={APS}
}

@article{hein2006entanglement,
  title={Entanglement in graph states and its applications},
  author={Hein, Marc and D{\"u}r, Wolfgang and Eisert, Jens and Raussendorf, Robert and Nest, M and Briegel, H-J},
  journal={arXiv preprint quant-ph/0602096},
  url={https://arxiv.org/abs/quant-ph/0602096},
  doi={10.48550/arXiv.quant-ph/0602096},
  year={2006}
}

@article{wilde2009logical,
  title={Logical operators of quantum codes},
  author={Wilde, Mark M},
  journal={Physical Review A},
  volume={79},
  number={6},
  pages={062322},
  year={2009},
  publisher={APS},
  doi={10.1103/PhysRevA.79.062322}
}

% Encoding circuits

@article{cleve1997efficient,
  title={Efficient computations of encodings for quantum error correction},
  author={Cleve, Richard and Gottesman, Daniel},
  journal={Physical Review A},
  volume={56},
  number={1},
  pages={76},
  year={1997},
  publisher={APS}
}

@inproceedings{grassl2011variations,
  title={Variations on encoding circuits for stabilizer quantum codes},
  author={Grassl, Markus},
  booktitle={International Conference on Coding and Cryptology},
  pages={142--158},
  year={2011},
  organization={Springer}
}

@article{grassl2002algorithmic,
  title={Algorithmic aspects of quantum error-correcting codes},
  author={Grassl, Markus},
  journal={Mathematics of Quantum Computation},
  pages={223--252},
  year={2002},
  publisher={CRC Press Boca Raton, FL}
}

% Examples of results that employ the tableaux formalism

@article{gullans2021quantum,
  title = {Quantum {{Coding}} with {{Low-Depth Random Circuits}}},
  author = {Gullans, Michael J. and Krastanov, Stefan and Huse, David A. and Jiang, Liang and Flammia, Steven T.},
  year = {2021},
  month = sep,
  journal = {Physical Review X},
  volume = {11},
  number = {3},
  pages = {031066},
  issn = {2160-3308},
  doi = {10.1103/PhysRevX.11.031066}
}

@article{krastanov2020heterogeneous,
  title={Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices},
  author={Krastanov, Stefan and de la Cerda, Alexander Sanchez and Narang, Prineha},
  journal={arXiv preprint arXiv:2011.11640},
  year={2020}
}

@article{nahum2017quantum,
	title = {Quantum Entanglement Growth under Random Unitary Dynamics},
	volume = {7},
	url = {https://link.aps.org/doi/10.1103/PhysRevX.7.031016},
	doi = {10.1103/PhysRevX.7.031016},
	pages = {031016},
	number = {3},
	journal = {Physical Review X},
	author = {Nahum, Adam and Ruhman, Jonathan and Vijay, Sagar and Haah, Jeongwan},
  year = {2017}
}

% minimum distance

@article{vardy1997intractability,
  title={The intractability of computing the minimum distance of a code},
  author={Vardy, Alexander},
  journal={IEEE Transactions on Information Theory},
  volume={43},
  number={6},
  pages={1757--1766},
  year={1997},
  publisher={IEEE}
}

@phdthesis{Sabo:2022smk,
  author = "Sabo, Eric",
  title = "{Trellis Decoding And Applications For Quantum Error Correction}",
  school = "Georgia Tech",
  year = "2022"
}

@article{kapshikar2023hardness,
  title={On the hardness of the minimum distance problem of quantum codes},
  author={Kapshikar, Upendra and Kundu, Srijita},
  journal={IEEE Transactions on Information Theory},
  volume={69},
  number={10},
  pages={6293--6302},
  year={2023},
  publisher={IEEE}
}

@inproceedings{white2006new,
  title={A new minimum weight algorithm for additive codes},
  author={White, Greg and Grassl, Markus},
  booktitle={2006 IEEE International Symposium on Information Theory},
  pages={1119--1123},
  year={2006},
  organization={IEEE}
}

@article{pryadko2023qdistrnd,
  title={QDistRnd: A GAP package for computing the distance of quantum error-correcting codes},
  author={Pryadko, Leonid P and Shabashov, Vadim A and Kozin, Valerii K},
  journal={arXiv preprint arXiv:2308.15140},
  year={2023}
}

@article{Lubin2023,
  title={JuMP 1.0: Recent improvements to a modeling language for mathematical optimization},
  author={Lubin, Miles and Dowson, Oscar and Garcia, Joaquim Dias and Huchette, Joey and Legat, Beno{\^\i}t and Vielma, Juan Pablo},
  journal={Mathematical Programming Computation},
  volume={15},
  number={3},
  pages={581--589},
  year={2023},
  publisher={Springer}
}

@article{makhorin2008glpk,
  title={GLPK (GNU linear programming kit)},
  author={Makhorin, Andrew},
  journal={http://www. gnu. org/s/glpk/glpk. html},
  year={2008}
}

@article{huangfu2018parallelizing,
  title={Parallelizing the dual revised simplex method},
  author={Huangfu, Qi and Hall, JA Julian},
  journal={Mathematical Programming Computation},
  volume={10},
  number={1},
  pages={119--142},
  year={2018},
  publisher={Springer}
}

@article{lacroix2024scaling,
  title={Scaling and logic in the color code on a superconducting quantum processor},
  author={Lacroix, Nathan and Bourassa, Alexandre and Heras, Francisco JH and Zhang, Lei M and Bausch, Johannes and Senior, Andrew W and Edlich, Thomas and Shutty, Noah and Sivak, Volodymyr and Bengtsson, Andreas and others},
  journal={arXiv preprint arXiv:2412.14256},
  url={https://arxiv.org/abs/2412.14256},
  year={2024}
}

@misc{cain2025correlateddecodinglogicalalgorithms,
  title={Correlated decoding of logical algorithms with transversal gates},
  author={Madelyn Cain and Chen Zhao and Hengyun Zhou and Nadine Meister and J. Pablo Bonilla Ataides and Arthur Jaffe and Dolev Bluvstein and Mikhail D. Lukin},
  year={2025},
  eprint={2403.03272},
  archivePrefix={arXiv},
  primaryClass={quant-ph},
  url={https://arxiv.org/abs/2403.03272},
}

@misc{wang2022distanceboundsgeneralizedbicycle,
  title={Distance bounds for generalized bicycle codes},
  author={Renyu Wang and Leonid P. Pryadko},
  year={2022},
  eprint={2203.17216},
  archivePrefix={arXiv},
  primaryClass={quant-ph},
  url={https://arxiv.org/abs/2203.17216},
}

% non-Clifford formalism

@misc{Yoder2012AGO,
  title = {A Generalization of the Stabilizer Formalism for Simulating Arbitrary Quantum Circuits},
  author = {Theodore J. Yoder},
  year = {2012},
  howpublished = {Semantic Scholar Corpus ID: 18406560},
  url = {https://api.semanticscholar.org/CorpusID:18406560},
  note = {Also available at \url{http://www.scottaaronson.com/showcase2/report/ted-yoder.pdf}}
}

% codes

@article{mackay2004sparse,
  title={Sparse-graph codes for quantum error correction},
  author={MacKay, David JC and Mitchison, Graeme and McFadden, Paul L},
  journal={IEEE Transactions on Information Theory},
  volume={50},
  number={10},
  pages={2315--2330},
  year={2004},
  publisher={IEEE},
  doi={10.1109/TIT.2004.834737}
}

@article{calderbank1998quantum,
  title={Quantum error correction via codes over GF (4)},
  author={Calderbank, A Robert and Rains, Eric M and Shor, PM and Sloane, Neil JA},
  journal={IEEE Transactions on Information Theory},
  volume={44},
  number={4},
  pages={1369--1387},
  year={1998},
  publisher={IEEE},
  doi={10.1109/18.681315}
}

@inproceedings{steane2007tutorial,
  title={A tutorial on quantum error correction},
  author={Steane, Andrew M},
  booktitle={PROCEEDINGS-INTERNATIONAL SCHOOL OF PHYSICS ENRICO FERMI},
  volume={162},
  pages={1},
  year={2007},
  organization={IOS Press; Ohmsha; 1999},
  doi={10.3254/978-1-61499-018-5-1}
}

@article{yu2013all,
  author={Yu, Sixia and Bierbrauer, Jürgen and Dong, Ying and Chen, Qing and Oh, C. H.},
  journal={IEEE Transactions on Information Theory},
  title={All the Stabilizer Codes of Distance 3},
  year={2013},
  volume={59},
  number={8},
  pages={5179-5185},
  keywords= {Generators;Frequency modulation;Vectors;Educational institutions;Error correction codes;Physics;Indexes;1-error correcting stabilizer codes;optimal codes;quantum error correction;quantum Hamming bound},
  doi={10.1109/TIT.2013.2259138}
}

@article{chao2018quantum,
  title={Quantum Error Correction with Only Two Extra Qubits.},
  author={Rui Chao and Ben W Reichardt},
  journal={Physical review letters},
  year={2017},
  volume={121 5},
  pages={
          050502
        },
  url={https://api.semanticscholar.org/CorpusID:206314271}
}

@article{gottesman1996class,
  title={Class of quantum error-correcting codes saturating the quantum Hamming bound},
  author={Gottesman, Daniel},
  journal={Physical Review A},
  volume={54},
  number={3},
  pages={1862},
  year={1996},
  publisher={APS}
}

@article{kitaev2003fault,
	title = {Fault-tolerant quantum computation by anyons},
	volume = {303},
	issn = {00034916},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0003491602000180},
	doi = {10.1016/S0003-4916(02)00018-0},
	abstract = {A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.},
	pages = {2--30},
	number = {1},
  year = {2003},
  journal={Annals of Physics},
	journaltitle = {Annals of Physics},
	shortjournal = {Annals of Physics},
	author = {Kitaev, A.Yu.}
}

@article{fowler2012surface,
	title = {Surface codes: Towards practical large-scale quantum computation},
	volume = {86},
	issn = {1050-2947, 1094-1622},
	url = {https://link.aps.org/doi/10.1103/PhysRevA.86.032324},
	doi = {10.1103/PhysRevA.86.032324},
	shorttitle = {Surface codes},
	pages = {032324},
	number = {3},
  year = {2012},
  journal={Physical Review A},
	journaltitle = {Physical Review A},
	shortjournal = {Phys. Rev. A},
	author = {Fowler, Austin G. and Mariantoni, Matteo and Martinis, John M. and Cleland, Andrew N.},
}

@article{muller1954application,
  title={Application of Boolean algebra to switching circuit design and to error detection},
  author={Muller, David E},
  journal={Transactions of the IRE professional group on electronic computers},
  number={3},
  pages={6--12},
  year={1954},
  publisher={IEEE}
}

@article{reed1954class,
  title={A class of multiple-error-correcting codes and the decoding scheme},
  author={Reed, Irving S},
  journal={IEEE Transactions on Information Theory},
  volume={4},
  number={4},
  pages={38--49},
  year={1954}
}

@article{raaphorst2003reed,
  title={Reed-muller codes},
  author={Raaphorst, Sebastian},
  journal={Carleton University, May},
  volume={9},
  year={2003},
  publisher={Citeseer}
}

@article{abbe2020reed,
  title={Reed--Muller codes: Theory and algorithms},
  author={Abbe, Emmanuel and Shpilka, Amir and Ye, Min},
  journal={IEEE Transactions on Information Theory},
  volume={67},
  number={6},
  pages={3251--3277},
  year={2020},
  publisher={IEEE}
}

@book{djordjevic2021quantum,
  title={Quantum information processing, quantum computing, and quantum error correction: an engineering approach},
  author={Djordjevic, Ivan B},
  year={2021},
  publisher={Academic Press}
}

@article{hocquenghem1959codes,
  title={Codes correcteurs d'erreurs},
  author={Hocquenghem, Alexis},
  journal={Chiffers},
  volume={2},
  pages={147--156},
  year={1959}
}

@article{bose1960class,
  title={On a class of error correcting binary group codes},
  author={Bose, Raj Chandra and Ray-Chaudhuri, Dwijendra K},
  journal={Information and control},
  volume={3},
  number={1},
  pages={68--79},
  year={1960},
  publisher={Elsevier}
}

@article{bose1960further,
  title={Further results on error correcting binary group codes},
  author={Bose, Raj Chandra and Ray-Chaudhuri, Dwijendra K},
  journal={Information and Control},
  volume={3},
  number={3},
  pages={279--290},
  year={1960},
  publisher={Elsevier}
}

@book{error2024lin,
  title={Error Control Coding},
  author={Lin, Shu and Costello, Daniel},
  year={2024},
  publisher={Pearson}
}

@article{knill1996concatenated,
  title={Concatenated quantum codes},
  author={Knill, Emanuel and Laflamme, Raymond},
  journal={arXiv preprint quant-ph/9608012},
  year={1996}
}

@inproceedings{brown2013short,
  title = {Short Random Circuits Define Good Quantum Error Correcting Codes},
  booktitle = {2013 {{IEEE International Symposium}} on {{Information Theory}}},
  author = {Brown, Winton and Fawzi, Omar},
  year = {2013},
  month = jul,
  pages = {346--350},
  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},
  year = {2021},
  month = nov,
  journal = {Quantum},
  volume = {5},
  eprint = {1904.02703},
  primaryclass = {quant-ph},
  pages = {585},
  issn = {2521-327X},
  doi = {10.22331/q-2021-11-22-585},
  archiveprefix = {arXiv}
}


@inproceedings{panteleev2022asymptotically,
  title = {Asymptotically Good {{Quantum}} and Locally Testable Classical {{LDPC}} Codes},
  booktitle = {Proceedings of the 54th {{Annual ACM SIGACT Symposium}} on {{Theory}} of {{Computing}}},
  author = {Panteleev, Pavel and Kalachev, Gleb},
  year = {2022},
  month = jun,
  pages = {375--388},
  publisher = {ACM},
  address = {Rome Italy},
  doi = {10.1145/3519935.3520017},
  isbn = {978-1-4503-9264-8}
}

@article{roffe2023bias,
  title = {Bias-Tailored Quantum {{LDPC}} Codes},
  author = {Roffe, Joschka and Cohen, Lawrence Z. and Quintavalle, Armanda O. and Chandra, Daryus and Campbell, Earl T.},
  year = {2023},
  month = may,
  journal = {Quantum},
  volume = {7},
  pages = {1005},
  doi = {10.22331/q-2023-05-15-1005}
}

@article{raveendran2022finite,
  title = {Finite {{Rate QLDPC-GKP Coding Scheme}} That {{Surpasses}} the {{CSS Hamming Bound}}},
  author = {Raveendran, Nithin and Rengaswamy, Narayanan and Rozp{\k e}dek, Filip and Raina, Ankur and Jiang, Liang and Vasi{\'c}, Bane},
  year = {2022},
  month = jul,
  journal = {Quantum},
  volume = {6},
  pages = {767},
  issn = {2521-327X},
  doi = {10.22331/q-2022-07-20-767},
}

@article{steane1999quantum,
  title={Quantum reed-muller codes},
  author={Steane, Andrew M},
  journal={IEEE Transactions on Information Theory},
  volume={45},
  number={5},
  pages={1701--1703},
  year={1999},
  publisher={IEEE}
}

@article{campbell2012magic,
  title={Magic-state distillation in all prime dimensions using quantum reed-muller codes},
  author={Campbell, Earl T and Anwar, Hussain and Browne, Dan E},
  journal={Physical Review X},
  volume={2},
  number={4},
  pages={041021},
  year={2012},
  publisher={APS}
}

@article{anderson2014fault,
  title={Fault-tolerant conversion between the steane and reed-muller quantum codes},
  author={Anderson, Jonas T and Duclos-Cianci, Guillaume and Poulin, David},
  journal={Physical review letters},
  volume={113},
  number={8},
  pages={080501},
  year={2014},
  publisher={APS}
}

@article{lin2024quantum,
  title={Quantum two-block group algebra codes},
  author={Lin, Hsiang-Ku and Pryadko, Leonid P},
  journal={Physical Review A},
  volume={109},
  number={2},
  pages={022407},
  year={2024},
  publisher={APS}
}

@article{wang2024coprime,
  title={Coprime Bivariate Bicycle Codes and their Properties},
  author={Wang, Ming and Mueller, Frank},
  journal={arXiv preprint arXiv:2408.10001},
  year={2024}
}

@misc{voss2024multivariatebicyclecodes,
  title={Multivariate Bicycle Codes},
  author={Lukas Voss and Sim Jian Xian and Tobias Haug and Kishor Bharti},
  year={2024},
  eprint={2406.19151},
  archivePrefix={arXiv},
  primaryClass={quant-ph},
  url={https://arxiv.org/abs/2406.19151},
}

@article{bravyi2024high,
  title={High-threshold and low-overhead fault-tolerant quantum memory},
  author={Bravyi, Sergey and Cross, Andrew W and Gambetta, Jay M and Maslov, Dmitri and Rall, Patrick and Yoder, Theodore J},
  journal={Nature},
  volume={627},
  number={8005},
  pages={778--782},
  year={2024},
  publisher={Nature Publishing Group UK London}
}

@article{haah2011local,
  title={Local stabilizer codes in three dimensions without string logical operators},
  author={Haah, Jeongwan},
  journal={Physical Review A?Atomic, Molecular, and Optical Physics},
  volume={83},
  number={4},
  pages={042330},
  year={2011},
}

@inproceedings{wang2023abelian,
  title={Abelian and non-Abelian quantum two-block codes},
  author={Wang, Renyu and Lin, Hsiang-Ku and Pryadko, Leonid P},
  booktitle={2023 12th International Symposium on Topics in Coding (ISTC)},
  pages={1--5},
  year={2023},
  organization={IEEE}
}

@article{naghipour2015quantum,
  title={Quantum stabilizer codes from Abelian and non-Abelian groups association schemes},
  author={Naghipour, Avaz and Jafarizadeh, Mohammad Ali and Shahmorad, Sedaghat},
  journal={International Journal of Quantum Information},
  volume={13},
  number={03},
  pages={1550021},
  year={2015},
  publisher={World Scientific}
}

@article{golay1949notes,
  title={Notes on digital coding},
  author={Golay, Marcel JE},
  journal={Proc. IEEE},
  volume={37},
  pages={657},
  year={1949}
}

@book{huffman2010fundamentals,
  title={Fundamentals of error-correcting codes},
  author={Huffman, W Cary and Pless, Vera},
  year={2010},
  publisher={Cambridge university press}
}

@article{bhatia2018mceliece,
  title={McEliece cryptosystem based on extended Golay code},
  author={Bhatia, Amandeep Singh and Kumar, Ajay},
  journal={arXiv preprint arXiv:1811.06246},
  year={2018}
}

@misc{landahl2011color,
  title={Fault-tolerant quantum computing with color codes},
  author={Andrew J. Landahl and Jonas T. Anderson and Patrick R. Rice},
  year={2011},
  eprint={1108.5738},
  archivePrefix={arXiv},
  primaryClass={quant-ph},
  url={https://arxiv.org/abs/1108.5738},
}
