dorsal/arxiv
View SchemaThe Quantum Schur Transform: I. Efficient Qudit Circuits
| Authors | Dave Bacon, Isaac L. Chuang, Aram W. Harrow |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601001 |
| URL | https://arxiv.org/abs/quant-ph/0601001 |
| Journal | Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms (SODA), pp. 1235-1244, 2007. |
Abstract
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of epsilon, then our circuit construction uses a number of gates which is polynomial in n, d and log(1/epsilon). The important insights we use to perform this construction are the selection of the appropriate subgroup adapted basis and the Wigner-Eckart theorem. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and is an important new efficient quantum circuit family which goes significantly beyond the standard paradigm of the quantum Fourier transform.
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"abstract": "We present an efficient family of quantum circuits for a fundamental\nprimitive in quantum information theory, the Schur transform. The Schur\ntransform on n d-dimensional quantum systems is a transform between a standard\ncomputational basis to a labelling related to the representation theory of the\nsymmetric and unitary groups. If we desire to implement the Schur transform to\nan accuracy of epsilon, then our circuit construction uses a number of gates\nwhich is polynomial in n, d and log(1/epsilon). The important insights we use\nto perform this construction are the selection of the appropriate subgroup\nadapted basis and the Wigner-Eckart theorem. Our efficient circuit construction\nrenders numerous protocols in quantum information theory computationally\ntractable and is an important new efficient quantum circuit family which goes\nsignificantly beyond the standard paradigm of the quantum Fourier transform.",
"arxiv_id": "quant-ph/0601001",
"authors": [
"Dave Bacon",
"Isaac L. Chuang",
"Aram W. Harrow"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proceedings of the eighteenth annual ACM-SIAM symposium on\n Discrete algorithms (SODA), pp. 1235-1244, 2007.",
"title": "The Quantum Schur Transform: I. Efficient Qudit Circuits",
"url": "https://arxiv.org/abs/quant-ph/0601001"
},
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