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We give a finite presentation by generators and relations of the unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators.
Graduate Texts in Mathematics, Springer, New York, NY, USA
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Cambridge University Press, New York, NY, USA
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Journal of Pure and Applied Algebra
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Available at http://arxiv.org/abs/0806.3834
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In Bob Coecke, editor: New Structures for Physics
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Matthew Amy, Dmitri Maslov, Michele Mosca & Martin Roetteler (2013): A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits · 2013
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Brett Giles & Peter Selinger (2013): Exact synthesis of multiqubit Clifford+T circuits · 2013
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Vadym Kliuchnikov, Dmitri Maslov & Michele Mosca (2013): Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates · 2013
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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David Gosset, Vadym Kliuchnikov, Michele Mosca & Vincent Russo (2014): An Algorithm for the T-count · 2014
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Available at http://arxiv.org/abs/1601.07363
Matthew Amy & Michele Mosca (2016): T-count optimization and Reed-Muller codes · 2016
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In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, PawełSobociński & Fabio Zanasi (2016): Rewriting Modulo Symmetric Monoidal Structure · 2016
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Andrew W Cross, Easwar Magesan, Lev S Bishop, John A Smolin & Jay M Gambetta (2016): Scalable randomised benchmarking of non-Clifford gates · 2016
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Available at http://arxiv.org/abs/1606.01904
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Ryan O’Donnell (2014): Analysis of Boolean Functions · 2014
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Peter Selinger (2015): Generators and Relations for n-Qubit Clifford Operators · 2015
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Neil J. Ross & Peter Selinger (2016): Optimal ancilla-free Clifford+T approximation of z -rotations · 2016
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