Quantum Coupon Collector

@article{Arunachalam2020QuantumCC,
  title={Quantum Coupon Collector},
  author={Srinivasan Arunachalam and A. Belovs and Andrew M. Childs and Robin Kothari and A. Rosmanis and R. D. Wolf},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.07688}
}
We study how efficiently a $k$-element set $S\subseteq[n]$ can be learned from a uniform superposition $|S\rangle$ of its elements. One can think of $|S\rangle=\sum_{i\in S}|i\rangle/\sqrt{|S|}$ as the quantum version of a uniformly random sample over $S$, as in the classical analysis of the ``coupon collector problem.'' We show that if $k$ is close to $n$, then we can learn $S$ using asymptotically fewer quantum samples than random samples. In particular, if there are $n-k=O(1)$ missing… Expand
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