dorsal/arxiv
View SchemaPhase map decompositions for unitaries
| Authors | Niel de Beaudrap, Vincent Danos, Elham Kashefi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603266 |
| URL | https://arxiv.org/abs/quant-ph/0603266 |
Abstract
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based model for quantum computing. Specifically, we show how to extract from such a decomposition a matching entangled graph state (with inputs), and a set of measurements angles, when there is one. Next, we check whether the obtained graph state verifies a "flow" condition, which guarantees an execution order such that the dependent measurements and corrections of the pattern yield deterministic results. Using a graph theoretic characterization of flows, we can determine whether a flow can be constructed for a graph state in polynomial time. This approach yields an algorithmic procedure which, when it succeeds, may produce an efficient pattern for a given unitary.
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"date_created": "2026-03-02T18:02:27.547000Z",
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"abstract": "We propose a universal decomposition of unitary maps over a tensorial power\nof C^2, introducing the key concept of \"phase maps\", and investigate how this\ndecomposition can be used to implement unitary maps directly in the\nmeasurement-based model for quantum computing. Specifically, we show how to\nextract from such a decomposition a matching entangled graph state (with\ninputs), and a set of measurements angles, when there is one. Next, we check\nwhether the obtained graph state verifies a \"flow\" condition, which guarantees\nan execution order such that the dependent measurements and corrections of the\npattern yield deterministic results. Using a graph theoretic characterization\nof flows, we can determine whether a flow can be constructed for a graph state\nin polynomial time. This approach yields an algorithmic procedure which, when\nit succeeds, may produce an efficient pattern for a given unitary.",
"arxiv_id": "quant-ph/0603266",
"authors": [
"Niel de Beaudrap",
"Vincent Danos",
"Elham Kashefi"
],
"categories": [
"quant-ph"
],
"title": "Phase map decompositions for unitaries",
"url": "https://arxiv.org/abs/quant-ph/0603266"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "70b44c0d-b561-4518-989c-38a25460f489",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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