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Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors.
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For example, the uniform distribution over the n n -qubit Clifford group is the most widely-used unitary 2-design Dankert et al. 2009 and a typical n n -qubit Clifford gate requires O [ n 2 / l o g ( n ) ] O[n^{2}/\mathop{log}\nolimits(n)] two-qubit gates to implement Aaronson and Gottesman 2004
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2018
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2019
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2021
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2021
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2021
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2021
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2021
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2022
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2022
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