Uniform superpositions with random binary phases are exponentially close in trace distance to Haar-random states for polynomially many copies, enabling pseudorandom quantum state constructions from post-quantum PRFs and low-depth t-designs.
Random quantum circuits are approximate 2-designs
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(Pseudo) Random Quantum States with Binary Phase
Uniform superpositions with random binary phases are exponentially close in trace distance to Haar-random states for polynomially many copies, enabling pseudorandom quantum state constructions from post-quantum PRFs and low-depth t-designs.