# Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom

@article{Grewal2022LowStabilizerComplexityQS, title={Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom}, author={Sabee Grewal and Vishnu Iyer and William Kretschmer and Daniel Liang}, journal={ArXiv}, year={2022}, volume={abs/2209.14530} }

We show that quantum states with “low stabilizer complexity” can be eﬃciently distinguished from Haar-random. Speciﬁcally, given an n -qubit pure state | ψ i , we give an eﬃcient algorithm that distinguishes whether | ψ i is (i) Haar-random or (ii) a state with stabilizer ﬁdelity at least 1 k (i.e., has ﬁdelity at least 1 k with some stabilizer state), promised that one of these is the case. With black-box access to | ψ i , our algorithm uses O (cid:0) k 12 log(1 /δ ) (cid:1) copies of | ψ i…

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