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We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random.
Self-Testing/Correcting with Applications to Numerical Problems
Manuel Blum, Michael Luby, and Ronitt Rubinfeld · 1993
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Scheme for reducing decoherence in quantum computer memory
Peter W. Shor · 1995
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Good quantum error-correcting codes exist
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Michael A. Nielsen and Isaac Chuang · 2002
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Zhengfeng Ji, Yi-Kai Liu, and Fang Song · 2018
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Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard · 2019
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Zvika Brakerski and Omri Shmueli · 2019
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Patrick Rall, Daniel Liang, Jeremy Cook, and William Kretschmer · 2019
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Hsin-Yuan Huang, Richard Kueng, and John Preskill · 2020
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Schur–Weyl duality for the Clifford group with applications: Property testing, a robust Hudson theorem, and de Finetti representations
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