On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems

@article{Childs2005OnTQ,
  title={On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems},
  author={Andrew M. Childs and P. Wocjan},
  journal={Quantum Information \& Computation},
  year={2005},
  volume={7},
  pages={504-521}
}
We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more natural than viewing the problem as a hidden subgroup problem. We prove that the hidden shift approach to rigid graph isomorphism is hard in two senses. First, we prove that Ω(n) copies of the hidden shift states are necessary to solve the problem (whereas O(n… Expand
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