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We establish lower-bounds on the number of resource states, also known as magic states, needed to perform various quantum computing tasks, treating stabilizer operations as free.
Producing an N+1 Qubit CCZ State with an N Qubit Adder
Craig Gidney · 1906
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Elementary gates for quantum computation
Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter · 1995
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Approximation by Quantum Circuits
Emanuel Knill · 1995
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A fast quantum mechanical algorithm for database search
Lov K. Grover · 1996
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Richard Cleve and Daniel Gottesman · 1997
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Vivek V. Shende, Igor L. Markov, and Stephen S. Bullock · 2004
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Smaller two-qubit circuits for quantum communication and computation
Vivek V. Shende, Igor L. Markov, and Stephen S. Bullock · 2004
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Sergey Bravyi and Alexei Kitaev · 2005
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Emanuel Knill · 2005
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V. V. Shende, S. S. Bullock, and I. L. Markov · 2005
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Number Theory: Volume I: Tools and Diophantine Equations
H. Cohen · 2007
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Restrictions on transversal encoded quantum gate sets
Bryan Eastin and Emanuel Knill · 2009
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Catalysis and activation of magic states in fault-tolerant architectures
Earl T. Campbell · 2011
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Surface codes: Towards practical large-scale quantum computation
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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Classification of topologically protected gates for local stabilizer codes
Sergey Bravyi and Robert König · 2013
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Low-overhead constructions for the fault-tolerant toffoli gate
Cody Jones · 2013
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Multilevel distillation of magic states for quantum computing
Cody Jones · 2013
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Quantum circuits of t t -depth one
Peter Selinger · 2013
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D Gosset, V Kliuchnikov, M Mosca, and V Russo · 2014
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Application of a resource theory for magic states to fault-tolerant quantum computing
Mark Howard and Earl T. Campbell · 2017
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Torsten Karzig, Christina Knapp, Roman M. Lutchyn, Parsa Bonderson, Matthew B. Hastings, Chetan Nayak, Jason Alicea, Karsten Flensberg, Stephan Plugge, Yuval Oreg, Charles M. Marcus, and Michael H. Freedman · 2017
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Convex geometry of quantum resource quantification
Bartosz Regula · 2017
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Simulation of quantum circuits by low-rank stabilizer decompositions
Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard · 2018
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Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
Craig Gidney and Austin G. Fowler · 2018
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Quantikz
Alastair Kay · 2018
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Approximate quantum fourier transform with o(nlog(n)) T gates
Yunseong Nam, Yuan Su, and Dmitri Maslov · 2018
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Efficiently computable bounds for magic state distillation
Xin Wang, Mark M Wilde, and Yuan Su · 2018
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T-count optimization and Reed-Muller codes
Matthew Amy and Michele Mosca · 2019
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Thomas G. Draper and Samuel A. Kutin · 2019
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