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Quantum Time Lower Bounds by Permutation Invariance
arXiv:2606.05099v1 Announce Type: cross Abstract: Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample...
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