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Note that the condition n ≥ f(k, t/2) ensures n ≥ 3 2(k2 − 3k + 26 + log 16

Hence, a sufficient condition for applying Theorem 16 in this case is n ≥ 3 2(k2 − 3k + 26 + log 16 15)

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Non-Clifford Cost of Random Unitaries

quant-ph · 2025-05-15 · unverdicted · novelty 6.0

Rigorous bounds establish that t = Theta(k^2) non-Clifford gates are necessary and sufficient for frame-potential approximation to unitary k-designs while t = Theta(nk) suffices for relative-error k-designs.

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  • Non-Clifford Cost of Random Unitaries quant-ph · 2025-05-15 · unverdicted · none · ref 2

    Rigorous bounds establish that t = Theta(k^2) non-Clifford gates are necessary and sufficient for frame-potential approximation to unitary k-designs while t = Theta(nk) suffices for relative-error k-designs.