@article(Aaronson2004ImprovedSO,
author = {Scott Aaronson and Daniel Gottesman},
year = {2004},
title = {Improved simulation of stabilizer circuits},
journal = {Physical Review A},
volume = {70},
pages = {052328},
doi = {10.1103/PhysRevA.70.052328},
note = {Also available from \href{http://arxiv.org/abs/quant-ph/0406196}{arXiv:quant-ph/0406196}},
)
@inproceedings(Amy16,
author = {Matthew Amy and Jianxin Chen and J. Ross, Neil},
year = {2018},
title = {A finite presentation of {CNOT}-dihedral operators},
booktitle = {Proceedings of the 14th International Conference on Quantum Physics and Logic, QPL 2017, Nijmegen},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {266},
pages = {84--97},
doi = {10.4204/EPTCS.266.5},
)
@article(Amy2020NumberTheoreticCO,
author = {Matthew Amy and Andrew N. Glaudell and Neil J. Ross},
year = {2020},
title = {Number-theoretic characterizations of some restricted {Clifford}+{$T$} circuits},
journal = {{Quantum}},
volume = {4},
pages = {252},
doi = {10.22331/q-2020-04-06-252},
note = {Also available from \href{http://arxiv.org/abs/1908.06076}{arXiv:1908.06076}},
)
@article(Backens2014TheZI,
author = {Miriam Backens},
year = {2014},
title = {The {ZX}-calculus is complete for stabilizer quantum mechanics},
journal = {New Journal of Physics},
volume = {16},
number = {9},
pages = {093021},
doi = {10.1088/1367-2630/16/9/093021},
note = {Also available from \href{http://arxiv.org/abs/1307.7025}{arXiv:1307.7025}},
)
@inproceedings(BK2019,
author = {Miriam Backens and Aleks Kissinger},
year = {2019},
title = {{ZH: A complete graphical calculus for quantum computations involving classical non-linearity}},
booktitle = {Proceedings of the 15th International Conference on Quantum Physics and Logic, QPL 2018, Halifax},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {287},
pages = {23--42},
doi = {10.4204/EPTCS.287.2},
)
@article(Bravyi2020HadamardfreeCE,
author = {Sergey Bravyi and Dmitri Maslov},
year = {2021},
title = {Hadamard-free circuits expose the structure of the {Clifford} group},
journal = {IEEE Transactions on Information Theory},
volume = {67},
number = {7},
pages = {4546--4563},
doi = {10.1109/TIT.2021.3081415},
note = {Also available from \href{http://arxiv.org/abs/2003.09412}{arXiv:2003.09412}},
)
@unpublished(Comfort19,
author = {Cole Comfort},
year = {2019},
title = {Circuit relations for real stabilizers: Towards {TOF+H}},
note = {Available from \href{http://arxiv.org/abs/1904.10614}{arXiv:1904.10614}},
)
@inproceedings(DP3,
author = {Ross Duncan and Simon Perdrix},
year = {2014},
title = {Pivoting makes the {ZX}-calculus complete for real stabilizers},
booktitle = {Proceedings of the 10th International Conference on Quantum Physics and Logic, QPL 2013},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {171},
pages = {50--62},
doi = {10.4204/EPTCS.171.5},
)
@unpublished(Gottesman1998TheHR,
author = {Daniel Gottesman},
year = {1998},
title = {The {Heisenberg} representation of quantum computers},
note = {Available from \href{http://arxiv.org/abs/quant-ph/9807006}{arXiv:quant-ph/9807006}},
)
@article(Hashagen2018RealRB,
author = {A. K. Hashagen and S. T. Flammia and D. Gross and J. J. Wallman},
year = {2018},
title = {Real randomized benchmarking},
journal = {{Quantum}},
volume = {2},
pages = {85},
doi = {10.22331/q-2018-08-22-85},
note = {Also available from \href{http://arxiv.org/abs/1801.06121}{arXiv:1801.06121}},
)
@unpublished(SupplementRealStab,
author = {Justin Makary and Neil J. Ross and Peter Selinger},
year = {2021},
title = {Supplement: Generators and relations for real stabilizer operators},
note = {Available as an ancillary file from this paper's arXiv page},
)
@article(Nebe00,
author = {G. Nebe and E. M. Rains and N. J. A. Sloane},
year = {2001},
title = {The invariants of the {Clifford} groups},
journal = {Designs, Codes and Cryptography},
volume = {24},
doi = {10.1023/A:1011233615437},
note = {Also available from \href{http://arxiv.org/abs/math/0001038}{arXiv:math/0001038}},
)
@book(NielsenChuang,
author = {Michael A. Nielsen and Isaac L. Chuang},
year = {2000},
title = {{Quantum Computation and Quantum Information}},
series = {Cambridge Series on Information and the Natural Sciences},
publisher = {Cambridge University Press},
doi = {10.1017/CBO9780511976667},
)
@unpublished(calderbank,
author = {Narayanan Rengaswamy and Robert Calderbank and Swanand Kadhe and Henry D. Pfister},
year = {2019},
title = {Logical {Clifford} synthesis for stabilizer codes},
note = {Available from \href{http://arxiv.org/abs/1907.00310}{arXiv:1907.00310}},
)
@article(Selinger15,
author = {Peter Selinger},
year = {2015},
title = {Generators and relations for $n$-qubit {Clifford} operators},
journal = {Logical Methods in Computer Science},
volume = {11},
number = {10},
pages = {1--17},
doi = {10.2168/LMCS-11(2:10)2015},
)
@article(Nest2010ClassicalSO,
author = {Van Den Nest, Maarten},
year = {2010},
title = {Classical simulation of quantum computation, the {Gottesman}-{Knill} theorem, and slightly beyond},
journal = {Quantum Information \& Computation},
volume = {10},
number = {3},
pages = {258--271},
doi = {10.26421/QIC10.3-4-6},
)
@inproceedings(Vilmart2018AZW,
author = {Renaud Vilmart},
year = {2018},
title = {A {ZX}-calculus with triangles for {Toffoli}-{Hadamard}, {Clifford}+{T}, and beyond},
booktitle = {Proceedings of the 15th International Conference on Quantum Physics and Logic, QPL 2018, Halifax},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {287},
pages = {313--344},
doi = {10.4204/EPTCS.287.18},
)