dorsal/arxiv
View SchemaEfficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
| Authors | Dave Bacon, Isaac Chuang, Aram Harrow |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407082 |
| URL | https://arxiv.org/abs/quant-ph/0407082 |
| DOI | 10.1103/PhysRevLett.97.170502 |
| Journal | Phys. Rev. Lett., Vol. 97, 170502 (2006) |
Abstract
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. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.
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"abstract": "The Schur basis on n d-dimensional quantum systems is a generalization of the\ntotal angular momentum basis that is useful for exploiting symmetry under\npermutations or collective unitary rotations. We present efficient (size\npoly(n,d,log(1/\\epsilon)) for accuracy \\epsilon) quantum circuits for the Schur\ntransform, which is the change of basis between the computational and the Schur\nbases. These circuits are based on efficient circuits for the Clebsch-Gordan\ntransformation. We also present an efficient circuit for a limited version of\nthe Schur transform in which one needs only to project onto different Schur\nsubspaces. This second circuit is based on a generalization of phase estimation\nto any nonabelian finite group for which there exists a fast quantum Fourier\ntransform.",
"arxiv_id": "quant-ph/0407082",
"authors": [
"Dave Bacon",
"Isaac Chuang",
"Aram Harrow"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.97.170502",
"journal_ref": "Phys. Rev. Lett., Vol. 97, 170502 (2006)",
"title": "Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms",
"url": "https://arxiv.org/abs/quant-ph/0407082"
},
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