References

  1. Dorit Aharonov (2003): A simple proof that Toffoli and Hadamard are quantum universal. arXiv:quant-ph/0301040.
  2. M. Amy, D. Maslov & M. Mosca (2014): Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 33(10), pp. 1476–1489, doi:10.1109/TCAD.2014.2341953.
  3. M. Amy, D. Maslov, M. Mosca & M. Roetteler (2013): A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 32(6), pp. 818–830, doi:10.1109/TCAD.2013.2244643.
  4. M. Amy & M. Mosca (2016): T-count optimization and Reed-Muller codes. arXiv:1601.07363.
  5. Niel de Beaudrap: A toy theory of tensor networks for exact quantum algorithms. To appear.
  6. B. Coecke & R. Duncan (2008): Interacting quantum observables. In: Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, doi:10.1007/978-3-540-70583-3_25.
  7. B. Coecke & R. Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics. New Journal of Physics 13, pp. 043016, doi:10.1088/1367-2630/13/4/043016. arXiv:quant-ph/09064725.
  8. B. Coecke & A. Kissinger (2017): Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, doi:10.1017/9781316219317.
  9. Shawn X. Cui, Daniel Gottesman & Anirudh Krishna (2017): Diagonal gates in the Clifford hierarchy. Phys. Rev. A 95, pp. 012329, doi:10.1103/PhysRevA.95.012329.
  10. R. Duncan & S. Perdrix (2009): Graph states and the necessity of Euler decomposition. Mathematical Theory and Computational Practice, pp. 167–177, doi:10.1007/978-3-642-03073-4_18.
  11. R. Duncan & S. Perdrix (2010): Rewriting measurement-based quantum computations with generalised flow. In: Proceedings of ICALP, Lecture Notes in Computer Science. Springer, pp. 285–296, doi:10.1007/978-3-642-14162-1_24.
  12. Ross Duncan (2013): A graphical approach to measurement-based quantum computing. In: Chris Heunen, Mehrnoosh Sadrzadeh & Edward Grefenstette: Quantum Physics and Linguistics. OUP, doi:10.1093/acprof:oso/9780199646296.003.0003. arXiv:1203.6242 [quant-ph].
  13. Mariami Gachechiladze, Costantino Budroni & Otfried Gühne (2016): Extreme violation of local realism in quantum hypergraph states. Physical Review Letters 116(7), pp. 070401, doi:10.1103/PhysRevLett.116.070401.
  14. Amar Hadzihasanovic: The algebra of entanglement and the geometry of composition. PhD thesis. University of Oxford.
  15. Luke E Heyfron & Earl T Campbell (2018): An efficient quantum compiler that reduces T count. Quantum Science and Technology 4(1), pp. 015004, doi:10.1088/2058-9565/aad604.
  16. Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '18. ACM, New York, NY, USA, pp. 559–568, doi:10.1145/3209108.3209131.
  17. Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus. Electronic Proceedings in Theoretical Computer Science 266, pp. 23–57, doi:10.4204/EPTCS.266.2. Version 1 at arXiv:1702.00934v1.
  18. Aleks Kissinger, Alex Merry & Matvey Soloviev (2014): Pattern graph rewrite systems. Electronic Proceedings in Theoretical Computer Science 143, pp. 54–66, doi:10.4204/EPTCS.143.5.
  19. Aleks Kissinger & Vladimir Zamdzhiev (2015): Quantomatic: A proof assistant for diagrammatic reasoning. In: International Conference on Automated Deduction. Springer, pp. 326–336, doi:10.1007/978-3-319-21401-6_22.
  20. Jacob Miller & Akimasa Miyake (2016): Hierarchy of universal entanglement in 2D measurement-based quantum computation. Npj Quantum Information 12(16036), doi:10.1038/npjqi.2016.36.
  21. Kang Feng Ng & Quanlong Wang (2017): A universal completion of the ZX-calculus.
  22. R. Raussendorf, D.E. Browne & H.J. Briegel (2003): Measurement-based quantum computation on cluster states. Physical Review A 68(2), pp. 22312, doi:10.1103/PhysRevA.68.022312.
  23. M Rossi, D Bruß & C Macchiavello (2014): Hypergraph states in Grover's quantum search algorithm. Physica Scripta 2014(T160), pp. 014036, doi:10.1088/0031-8949/2014/T160/014036.
  24. Matteo Rossi, M Huber, D Bruß & C Macchiavello (2013): Quantum hypergraph states. New Journal of Physics 15(11), pp. 113022, doi:10.1088/1367-2630/15/11/113022.
  25. P. Selinger (2007): Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science 170, pp. 139–163, doi:10.1016/j.entcs.2006.12.018.
  26. Yaoyun Shi (2003): Both Toffoli and controlled-NOT Need Little Help to Do Universal Quantum Computing. Quantum Info. Comput. 3(1), pp. 84–92.

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