References

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

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