Realizable Hamiltonians for universal adiabatic quantum computers

Jacob D. Biamonte, Peter J. Love

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse σx σx coupling. We also show the universality and QMA-completeness of spin models with only one-local σz and σx fields and two-local σz σx interactions.

Original languageEnglish (US)
Article number012352
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume78
Issue number1
DOIs
StatePublished - Jul 28 2008

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quantum computers
EH-101 helicopter
quantum computation
completeness
Ising model
interactions

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Realizable Hamiltonians for universal adiabatic quantum computers",
abstract = "It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse σx σx coupling. We also show the universality and QMA-completeness of spin models with only one-local σz and σx fields and two-local σz σx interactions.",
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Realizable Hamiltonians for universal adiabatic quantum computers. / Biamonte, Jacob D.; Love, Peter J.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 78, No. 1, 012352, 28.07.2008.

Research output: Contribution to journalArticle

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AB - It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse σx σx coupling. We also show the universality and QMA-completeness of spin models with only one-local σz and σx fields and two-local σz σx interactions.

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