dorsal/arxiv
View SchemaGraph states as ground states of many-body spin-1/2 Hamiltonians
| Authors | M. Van den Nest, K. Luttmer, W. Dür, H. J. Briegel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612186 |
| URL | https://arxiv.org/abs/quant-ph/0612186 |
| DOI | 10.1103/PhysRevA.77.012301 |
| Journal | Phys. Rev. A 77, 012301 (2008) |
Abstract
We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, non-degenerate ground state. We determine for any graph state the minimal d such that it is the non-degenerate ground state of a d-body interaction Hamiltonian, while we show for d'-body Hamiltonians H with d'<d that the resulting ground state can only be close to the graph state at the cost of H having a small energy gap relative to the total energy. When allowing for ancilla particles, we show how to utilize a gadget construction introduced in the context of the k-local Hamiltonian problem, to obtain n-qubit graph states as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting on n'>n spins.
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"abstract": "We consider the problem whether graph states can be ground states of local\ninteraction Hamiltonians. For Hamiltonians acting on n qubits that involve at\nmost two-body interactions, we show that no n-qubit graph state can be the\nexact, non-degenerate ground state. We determine for any graph state the\nminimal d such that it is the non-degenerate ground state of a d-body\ninteraction Hamiltonian, while we show for d\u0027-body Hamiltonians H with d\u0027\u003cd\nthat the resulting ground state can only be close to the graph state at the\ncost of H having a small energy gap relative to the total energy. When allowing\nfor ancilla particles, we show how to utilize a gadget construction introduced\nin the context of the k-local Hamiltonian problem, to obtain n-qubit graph\nstates as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting\non n\u0027\u003en spins.",
"arxiv_id": "quant-ph/0612186",
"authors": [
"M. Van den Nest",
"K. Luttmer",
"W. D\u00fcr",
"H. J. Briegel"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.77.012301",
"journal_ref": "Phys. Rev. A 77, 012301 (2008)",
"title": "Graph states as ground states of many-body spin-1/2 Hamiltonians",
"url": "https://arxiv.org/abs/quant-ph/0612186"
},
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