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Pseudorandom unitaries are neither real nor sparse nor noise-robust
March 6, 2024, 5:11 a.m. | Tobias Haug, Kishor Bharti, Dax Enshan Koh
cs.CR updates on arXiv.org arxiv.org
Abstract: Pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs) possess the dual nature of being efficiently constructible while appearing completely random to any efficient quantum algorithm. In this study, we establish fundamental bounds on pseudorandomness. We show that PRSs and PRUs exist only when the probability that an error occurs is negligible, ruling out their generation on noisy intermediate-scale and early fault-tolerant quantum computers. Further, we show that PRUs need imaginarity while PRS do not have …
algorithm arxiv cs.cc cs.cr nature noise quant-ph quantum random real states study
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