dorsal/arxiv
View SchemaThe Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
| Authors | Jeroen Dehaene, Bart De Moor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304125 |
| URL | https://arxiv.org/abs/quant-ph/0304125 |
| DOI | 10.1103/PhysRevA.68.042318 |
| Journal | Phys. Rev. A 68, 042318 (2003) |
Abstract
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation and possibly quantum computing.
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"abstract": "We describe stabilizer states and Clifford group operations using linear\noperations and quadratic forms over binary vector spaces. We show how the\nn-qubit Clifford group is isomorphic to a group with an operation that is\ndefined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic\nforms. As an application we give two schemes to efficiently decompose Clifford\ngroup operations into one and two-qubit operations. We also show how the\ncoefficients of stabilizer states and Clifford group operations in a standard\nbasis expansion can be described by binary quadratic forms. Our results are\nuseful for quantum error correction, entanglement distillation and possibly\nquantum computing.",
"arxiv_id": "quant-ph/0304125",
"authors": [
"Jeroen Dehaene",
"Bart De Moor"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042318",
"journal_ref": "Phys. Rev. A 68, 042318 (2003)",
"title": "The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)",
"url": "https://arxiv.org/abs/quant-ph/0304125"
},
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