Quantum Mechanical Algorithms for the Nonabelian Hidden Subgroup Problem

We provide positive and negative results concerning the “standard method” of identifying a hidden subgroup of a nonabelian group using a quantum computer.

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Correspondence to Michelangelo Grigni.

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* Supported in part by NSF grants CCR-9820931 and CCR-0208929.

† Supported in part by NSF CAREER grant 0049092, the NSF Institute for Quantum Information, the Charles Lee Powell Foundation, and the Mathematical Sciences Research Institute.

‡ Supported in part by an NSF Mathematical Sciences Postdoctoral Research Fellowship and NSF grant DMS-0301320.

§ Supported in part by DARPA QUIST grant F30602-01-2-0524, ARO grant DAAD19-03-1-0082, and NSF ITR grant CCR-0121555.

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Grigni, M., Schulman, L., Vazirani, M. et al. Quantum Mechanical Algorithms for the Nonabelian Hidden Subgroup Problem. Combinatorica 24, 137–154 (2004). https://doi.org/10.1007/s00493-004-0009-8

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Mathematics Subject Classification (2000):

  • 81P68
  • 68Q17