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In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and $\pi/2$-phase rotations, together with T operations ($\pi/4$-phase rotations).
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Ross Duncan, Aleks Kissinger, Simon Perdrix & John van de Wetering (2019): Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus · 1902
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Simon Perdrix Emmanuel Jeandel & Renaud Vilmart (2019): Completeness of the ZX-Calculus · 1903
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Aleks Kissinger & John van de Wetering (2019): Reducing T-count with the ZX-calculus · 1903
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Fang Zhang & Jianxin Chen (2019): Optimizing T gates in Clifford+T circuit as π / 4 \pi/4 rotations around Paulis · 1903
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C. Horsman, A. G Fowler, S. Devitt & R. Van Meter (2012): Surface code quantum computing by lattice surgery · 2012
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Quantum Science and Technology
Luke E. Heyfron & Earl T. Campbell (2018): An efficient quantum compiler that reduces T count · 2018
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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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Cody Jones (2013): Low-overhead constructions for the fault-tolerant Toffoli gate · 2013
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David Gosset, Vadym Kliuchnikov, Michele Mosca & Vincent Russo (2014): An Algorithm for the T-count · 2014
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Sergey Bravyi & David Gosset (2016): Improved classical simulation of quantum circuits dominated by Clifford gates · 2016
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Dalhousie University Mathstat Cluster: Available at https://www.mathstat.dal.ca/cluster/doku.php
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https://github.com/njross/optimizer
Yunseong Nam, Neil J. Ross, Yuan Su, Andrew M. Childs & Dmitri Maslov: “optimiser” Github
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Yunseong Nam, Neil J. Ross, Yuan Su, Andrew M. Childs & Dmitri Maslov (2018): Automated optimization of large quantum circuits with continuous parameters · 2018
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IEEE Transactions on Information Theory
Matthew Amy & Michele Mosca (2019): T-count optimization and Reed-Muller codes · 2019
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In: 34th Annual ACM/IEEE Symposium on Logic in Computer Science
Renaud Vilmart (2019): A Near-Optimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics · 2019
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Dmitri Maslov: Reversible Logic Synthesis Benchmarks page · 2020
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Matthew Amy, Dmitri Maslov & Michele Mosca (2014): Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning · 2042
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