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Spekkens' toy theory is a non-contextual hidden variable model with an epistemic restriction, a constraint on what the observer can know about the reality.
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D. Aharonov, A Simple Proof that Toffoli and Hadamard are Quantum Universal
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Y. Shi, Both Toffoli and Controlled-NOT need little help to do universal quantum computation
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S. Bravij, A. Kitaev Universal quantum computation with ideal Clifford gates and noisy ancillas
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R. W. Spekkens Contextuality for preparations, transformations, and unsharp measurements
2005
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D. Gross Hudson’s theorem for finite-dimensional quantum systems
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C. Cormick, E. F. Galvao, D. Gottesman, J. P. Paz, and A. O. Pittenger Classicality in discrete Wigner functions
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C. Jones, Novel constructions for the fault-tolerant Toffoli gate
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C. Jones, Composite Toffoli gate with two-round error detection
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A. Paetznick and B. W. Reichardt Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction
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M. Howard, J. Wallman, V. Veitch, J. Emerson Contextuality supplies the magic for quantum computation
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N. Delfosse, P. A. Guerin, J. Bian, and R. Raussendorf Wigner Function Negativity and Contextuality in Quantum Computation on Rebits
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R. W. Spekkens Evidence for the epistemic view of quantum states: A toy theory
2007
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R. W. Spekkens Negativity and Contextuality are Equivalent Notions of Nonclassicality
2008
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M. J. Bremner, R. Jozsa, D. J. Shepherd Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
2010
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N. Harrigan and R. W. Spekkens Einstein, Incompleteness, and the Epistemic View of Quantum States
2010
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J. J. Wallman, S. D. Bartlett Non-negative subtheories and quasiprobability representations of qubits
2012
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V. Veitch, C. Ferrie, D. Gross, and J. Emerson Negative quasiprobability as a resource for quantum computation
2012
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2015
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R. W. Spekkens Quasi-quantization: classical statistical theories with an epistemic restriction
2016
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L. Catani and D. E. Browne Spekkens’ toy model in all dimensions and its relationship with stabilizer quantum mechanics
2017
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J. Bermejo-Vega, N. Delfosse, D.E. Browne, C. Okay, R. Raussendorf Contextuality as a Resource for Models of Quantum Computation with Qubits
2017
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R. Raussendorf, D.E. Browne, N. Delfosse, C. Okay, J. Bermejo-Vega Contextuality and Wigner function negativity in qubit quantum computation
2017
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C. Okay, S. Roberts, S. D. Bartlett and R. Raussendorf Topological proofs of contextuality in quantum mechanics
2017
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