A lattice problem in quantum NP

@article{Aharonov2003ALP,
  title={A lattice problem in quantum NP},
  author={Dorit Aharonov and Oded Regev},
  journal={44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.},
  year={2003},
  pages={210-219}
}
  • D. Aharonov, O. Regev
  • Published 30 July 2003
  • Mathematics
  • 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
We consider coGapSVP/sub /spl radic/n/, a gap version of the shortest vector in a lattice problem. This problem is known to be in AM /spl cap/ coNP but is not known to be in NP or in MA. We prove that it lies inside QMA, the quantum analogue of NP. This is the first non-trivial upper bound on the quantum complexity of a lattice problem. The proof relies on two novel ideas. First, we give a new characterization of QMA, called QMA+ formulation allows us to circumvent a problem which arises… 

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