Any approximate quantum state 2-design is unconditionally pseudorandom against QNC0 and AC0 after QNC0 adversaries, with analogous pseudoentanglement and parallel-query unitary-design results.
Quantum Pseudoentanglement
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Unconditional Pseudorandomness against Shallow Quantum Circuits
Any approximate quantum state 2-design is unconditionally pseudorandom against QNC0 and AC0 after QNC0 adversaries, with analogous pseudoentanglement and parallel-query unitary-design results.