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Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set.
Maximal orders
Irving Reiner · 1975
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Distillation of nonstabilizer states for universal quantum computation
Guillaume Duclos-Cianci and Krysta M. Svore · 1980
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Hecke operators and distributing points on the sphere I
A. Lubotzky, R. Phillips, and P. Sarnak · 1986
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Randomized algorithms in number theory
Michael O. Rabin and Jeffery O. Shallit · 1986
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Hecke operators and distributing points on S2. II
A. Lubotzky, R. Phillips, and P. Sarnak · 1987
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Efficient discrete approximations of quantum gates
Aram W. Harrow, Benjamin Recht, and Isaac L. Chuang · 2002
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Classical and Quantum Computation
Alexei Kitaev, Alexander Shen, and Mikhail Vyalyi · 2002
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Perfect Lattices in Euclidean Spaces
Jacques Martinet · 2003
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The Solovay-Kitaev algorithm
Christopher M. Dawson and Michael A. Nielsen · 2005
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Topological quantum compiling
Layla Hormozi, Georgios Zikos, Nicholas Bonesteel, and Steven H. Simon · 2007
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On the spectral gap for finitely-generated subgroups of SU (2)
Jean Bourgain and Alexander Gamburd · 2008
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Algorithmic enumeration of ideal classes for quaternion orders
Markus Kirschmer and John Voight · 2008
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Representation of Quantum Circuits with Clifford and pi/8 Gates
Ken Matsumoto and Kazuyuki Amano · 2008
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Computing fundamental domains for Fuchsian groups
John Voight · 2009
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Resource-Optimal Single-Qubit Quantum Circuits
Alex Bocharov and Krysta M. Svore · 2012
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Faster quantum chemistry simulation on fault-tolerant quantum computers
Remarks on Matsumoto and Amano’s normal form for single-qubit Clifford+T operators
Brett Giles and Peter Selinger · 2013
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David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo · 2013
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Distillation protocols for Fourier states in quantum computing
N. Cody Jones · 2013
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Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates
Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2013
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Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries
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N. Cody Jones, James D. Whitfield, Peter L. McMahon, Man-hong Yung, Rodney Van Meter, Alán Aspuru-Guzik, and Yoshihisa Yamamoto · 2012
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Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2012
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Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits
Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2012
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Efficient Clifford+T approximation of single-qubit operators
Peter Selinger · 2012
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Efficient Decomposition of Single-Qubit Gates into V Basis Circuits
Alex Bocharov, Yuri Gurevich, and Krysta M. Svore · 2013
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Euclidean totally definite quaternion fields over the rational field and over quadratic number fields
Jean-Paul Cerri, Jerome Chaubert, and Pierre Lezowski · 2013
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In preparation
Cited in the paper.
Optimal Ancilla-free Pauli+V Circuits for Axial Rotations
Andreas Blass, Alex Bocharov, and Yuri Gurevich
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Adam Paetznick and Krysta M. Svore · 2013
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Floating point representations in quantum circuit synthesis
Nathan Wiebe and Vadym Kliuchnikov · 2013
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Efficient Synthesis of Universal Repeat-Until-Success Circuits
Alex Bocharov, Martin Roetteler, and Krysta M Svore · 2014
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New methods for Quantum Compiling
Vadym Kliuchnikov · 2014
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Asymptotically Optimal Topological Quantum Compiling
Vadym Kliuchnikov, Alex Bocharov, and Krysta M. Svore · 2014
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Exact Synthesis of Single-qubit Unitaries over Clifford-cyclotomic Gate Sets
Simon Forest, David Gosset, Vadym Kliuchnikov, and David Mckinnon · 2015
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