Efficient quantum circuits for Schur and Clebsch-Gordan transforms.

@article{Bacon2006EfficientQC,
  title={Efficient quantum circuits for Schur and Clebsch-Gordan transforms.},
  author={Dave Bacon and Isaac L. Chuang and Aram Wettroth Harrow},
  journal={Physical review letters},
  year={2006},
  volume={97 17},
  pages={170502}
}
The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum… CONTINUE READING
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