dorsal/arxiv
View SchemaThe complexity of quantum spin systems on a two-dimensional square lattice
| Authors | Roberto Oliveira, Barbara M. Terhal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504050 |
| URL | https://arxiv.org/abs/quant-ph/0504050 |
| Journal | Quant. Inf, Comp. Vol. 8, No. 10, pp. 0900-0924 (2008) |
Abstract
The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.
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"abstract": "The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum\ncomputational class QMA, see quant-ph/0406180. In this paper we show that this\nimportant problem remains QMA-complete when the interactions of the 2-local\nHamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our\nresults are partially derived with novel perturbation gadgets that employ\nmediator qubits which allow us to manipulate k-local interactions. As a side\nresult, we obtain that quantum adiabatic computation using 2-local interactions\nrestricted to a 2-D square lattice is equivalent to the circuit model of\nquantum computation. Our perturbation method also shows how any stabilizer\nspace associated with a k-local stabilizer (for constant k) can be generated as\nan approximate ground-space of a 2-local Hamiltonian.",
"arxiv_id": "quant-ph/0504050",
"authors": [
"Roberto Oliveira",
"Barbara M. Terhal"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quant. Inf, Comp. Vol. 8, No. 10, pp. 0900-0924 (2008)",
"title": "The complexity of quantum spin systems on a two-dimensional square lattice",
"url": "https://arxiv.org/abs/quant-ph/0504050"
},
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