dorsal/arxiv
View SchemaStabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic
| Authors | Erik Hostens, Jeroen Dehaene, Bart De Moor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408190 |
| URL | https://arxiv.org/abs/quant-ph/0408190 |
| DOI | 10.1103/PhysRevA.71.042315 |
| Journal | Phys. Rev. A 71, 042315 (2005) |
Abstract
We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over the integers modulo d. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.
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"abstract": "We describe generalizations of the Pauli group, the Clifford group and\nstabilizer states for qudits in a Hilbert space of arbitrary dimension d. We\nexamine a link with modular arithmetic, which yields an efficient way of\nrepresenting the Pauli group and the Clifford group with matrices over the\nintegers modulo d. We further show how a Clifford operation can be efficiently\ndecomposed into one and two-qudit operations. We also focus in detail on\nstandard basis expansions of stabilizer states.",
"arxiv_id": "quant-ph/0408190",
"authors": [
"Erik Hostens",
"Jeroen Dehaene",
"Bart De Moor"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.71.042315",
"journal_ref": "Phys. Rev. A 71, 042315 (2005)",
"title": "Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic",
"url": "https://arxiv.org/abs/quant-ph/0408190"
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