dorsal/arxiv
View SchemaGeometric Strategy for the Optimal Quantum Search
| Authors | Akimasa Miyake, Miki Wadati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109109 |
| URL | https://arxiv.org/abs/quant-ph/0109109 |
| DOI | 10.1103/PhysRevA.64.042317 |
| Journal | Phys. Rev. A 64, 042317 (2001) |
Abstract
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a target state, an element of the computational basis, and such an initial state as overlaps equally, up to phases, with all the elements of the computational basis. Second, we calculate the entanglement through the algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to the submanifold formed by separable states in Segre embedding, and find that entanglement is used almost maximally for large $n$. The computational time seems to be optimized by the dynamics as the geodesic, running across entangled states away from the submanifold of separable states, rather than the amount of entanglement itself.
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"abstract": "We explore quantum search from the geometric viewpoint of a complex\nprojective space $CP$, a space of rays. First, we show that the optimal quantum\nsearch can be geometrically identified with the shortest path along the\ngeodesic joining a target state, an element of the computational basis, and\nsuch an initial state as overlaps equally, up to phases, with all the elements\nof the computational basis. Second, we calculate the entanglement through the\nalgorithm for any number of qubits $n$ as the minimum Fubini-Study distance to\nthe submanifold formed by separable states in Segre embedding, and find that\nentanglement is used almost maximally for large $n$. The computational time\nseems to be optimized by the dynamics as the geodesic, running across entangled\nstates away from the submanifold of separable states, rather than the amount of\nentanglement itself.",
"arxiv_id": "quant-ph/0109109",
"authors": [
"Akimasa Miyake",
"Miki Wadati"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.64.042317",
"journal_ref": "Phys. Rev. A 64, 042317 (2001)",
"title": "Geometric Strategy for the Optimal Quantum Search",
"url": "https://arxiv.org/abs/quant-ph/0109109"
},
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