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Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation.
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E. Wigner · 1932
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A fundamental property of quantum-mechanical entropy
Elliott H. Lieb and Mary Beth Ruskai · 1973
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A wigner-function formulation of finite-state quantum mechanics
William K Wootters · 1987
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Concentrating partial entanglement by local operations
Charles H. Bennett, Herbert J. Bernstein, Sandu Popescu, and Benjamin Schumacher · 1996
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Purification of noisy entanglement and faithful teleportation via noisy channels
Charles H. Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A. Smolin, and William K. Wootters · 1996
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Fault-tolerant quantum computation
Peter Shor · 1996
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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The heisenberg representation of quantum computers
Daniel Gottesman · 1998
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Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature?
Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki · 1998
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Entanglement measures and purification procedures
V. Vedral and M. B. Plenio · 1998
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
Daniel Gottesman and Isaac Chuang · 1999
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All the bell inequalities
Asher Peres · 1999
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Are the laws of entanglement theory thermodynamical?
Michał Horodecki, Jonathan Oppenheim, and Ryszard Horodecki · 2002
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Computable measure of entanglement
G. Vidal and R. F. Werner · 2002
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Reversible transformations from pure to mixed states and the unique measure of information
Michał Horodecki, Paweł Horodecki, and Jonathan Oppenheim · 2003
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Discrete phase space based on finite fields
Kathleen S. Gibbons, Matthew J. Hoffman, and William K. Wootters · 2004
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Negativity of the wigner function as an indicator of non-classicality
Anatole Kenfack and Karol Życzkowski · 2004
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Universal quantum computation with ideal clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 2005
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Logarithmic negativity: A full entanglement monotone that is not convex
M. B. Plenio · 2005
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Quantum Inf. Proc
B.W. Reichardt · 2005
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Hudson’s theorem for finite-dimensional quantum systems
D. Gross · 2006
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On asymptotic continuity of functions of quantum states
Barbara Synak-Radtke and Michal Horodecki · 2006
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Non-negative wigner functions in prime dimensions
D. Gross · 2007
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Bound states for magic state distillation in fault-tolerant quantum computation
Earl T. Campbell and Dan E. Browne · 2010
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Necessity of negativity in quantum theory
Christopher Ferrie, Ryan Morris, and Joseph Emerson · 2010
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Catalysis and activation of magic states in fault-tolerant architectures
Earl T. Campbell · 2011
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Qutrit magic state distillation
Hussain Anwar, Earl T Campbell, and Dan E Browne · 2012
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Magic-state distillation in all prime dimensions using quantum reed-muller codes
Earl T. Campbell, Hussain Anwar, and Dan E. Browne · 2012
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D. Gross, K. Audenaert, and J. Eisert · 2007
Cited alongside, same era.
Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
Christopher Ferrie and Joseph Emerson · 2008
Cited alongside, same era.
The resource theory of quantum reference frames: manipulations and monotones
Gilad Gour and Robert W Spekkens · 2008
Cited alongside, same era.
Restrictions on Transversal Encoded Quantum Gate Sets
Bryan Eastin and Emanuel Knill · 2009
Cited alongside, same era.
An introduction to quantum error correction and fault-tolerant quantum computation
Daniel Gottesman · 2009
Cited alongside, same era.
Measuring the quality of a quantum reference frame: The relative entropy of frameness
Gilad Gour, Iman Marvian, and Robert W. Spekkens · 2009
Cited alongside, same era.
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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Qudit versions of the qubit π / 8 \pi/8 gate
Mark Howard and Jiri Vala · 2012
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Positive wigner functions render classical simulation of quantum computation efficient
A. Mari and J. Eisert · 2012
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Negative quasi-probability as a resource for quantum computation
Victor Veitch, Christopher Ferrie, David Gross, and Joseph Emerson · 2012
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Non-negative subtheories and quasiprobability representations of qubits
Joel J. Wallman and Stephen D. Bartlett · 2012
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Distilling one-qubit magic states into toffoli states
Bryan Eastin · 2013
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(quantumness in the context of) resource theories
Michal Horodecki and Jonathan Oppenheim · 2013
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Distillation protocols for Fourier states in quantum computing
Cody Jones · 2013
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Distillation protocols for Fourier states in quantum computing
Adam M. Meier, Bryan Eastin, and Emanuel Knill · 2013
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Efficient simulation scheme for a class of quantum optics experiments with non-negative wigner representation
Victor Veitch, Nathan Wiebe, Christopher Ferrie, and Joseph Emerson · 2013
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