dorsal/arxiv
View SchemaA simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
| Authors | Stephen D. Bartlett, Terry Rudolph |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609002 |
| URL | https://arxiv.org/abs/quant-ph/0609002 |
| DOI | 10.1103/PhysRevA.74.040302 |
| Journal | Phys. Rev. A, 74, 040302(R) (2006) |
Abstract
We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.
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"abstract": "We present a simple quantum many-body system - a two-dimensional lattice of\nqubits with a Hamiltonian composed of nearest-neighbor two-body interactions -\nsuch that the ground state is a universal resource for quantum computation\nusing single-qubit measurements. This ground state approximates a cluster state\nthat is encoded into a larger number of physical qubits. The Hamiltonian we use\nis motivated by the projected entangled pair states, which provide a\ntransparent mechanism to produce such approximate encoded cluster states on\nsquare or other lattice structures (as well as a variety of other quantum\nstates) as the ground state. We show that the error in this approximation takes\nthe form of independent errors on bonds occurring with a fixed probability. The\nenergy gap of such a system, which in part determines its usefulness for\nquantum computation, is shown to be independent of the size of the lattice. In\naddition, we show that the scaling of this energy gap in terms of the coupling\nconstants of the Hamiltonian is directly determined by the lattice geometry. As\na result, the approximate encoded cluster state obtained on a hexagonal lattice\n(a resource that is also universal for quantum computation) can be shown to\nhave a larger energy gap than one on a square lattice with an equivalent\nHamiltonian.",
"arxiv_id": "quant-ph/0609002",
"authors": [
"Stephen D. Bartlett",
"Terry Rudolph"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.040302",
"journal_ref": "Phys. Rev. A, 74, 040302(R) (2006)",
"title": "A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0609002"
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