dorsal/arxiv
View SchemaGraphical description of the action of Clifford operators on stabilizer states
| Authors | Matthew B. Elliott, Bryan Eastin, Carlton M. Caves |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703278 |
| URL | https://arxiv.org/abs/quant-ph/0703278 |
| DOI | 10.1103/PhysRevA.77.042307 |
| Journal | Phys. Rev. A 77, 042307 (2008) |
Abstract
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.
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"abstract": "We introduce a graphical representation of stabilizer states and translate\nthe action of Clifford operators on stabilizer states into graph operations on\nthe corresponding stabilizer-state graphs. Our stabilizer graphs are\nconstructed of solid and hollow nodes, with (undirected) edges between nodes\nand with loops and signs attached to individual nodes. We find that local\nClifford transformations are completely described in terms of local\ncomplementation on nodes and along edges, loop complementation, and change of\nnode type or sign. Additionally, we show that a small set of equivalence rules\ngenerates all graphs corresponding to a given stabilizer state; we do this by\nconstructing an efficient procedure for testing the equality of any two\nstabilizer graphs.",
"arxiv_id": "quant-ph/0703278",
"authors": [
"Matthew B. Elliott",
"Bryan Eastin",
"Carlton M. Caves"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.77.042307",
"journal_ref": "Phys. Rev. A 77, 042307 (2008)",
"title": "Graphical description of the action of Clifford operators on stabilizer states",
"url": "https://arxiv.org/abs/quant-ph/0703278"
},
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