Nonperturbative k -body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

J. D. Biamonte

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k -body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.

Original languageEnglish (US)
Article number052331
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume77
Issue number5
DOIs
StatePublished - May 23 2008

Fingerprint

embedding
engineers
perturbation theory
energy levels
ground state
energy
interactions

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

@article{4f8f577dace942a09f99b4b420c865c5,
title = "Nonperturbative k -body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins",
abstract = "An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k -body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.",
author = "Biamonte, {J. D.}",
year = "2008",
month = "5",
day = "23",
doi = "10.1103/PhysRevA.77.052331",
language = "English (US)",
volume = "77",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Nonperturbative k -body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

AU - Biamonte, J. D.

PY - 2008/5/23

Y1 - 2008/5/23

N2 - An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k -body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.

AB - An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k -body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.

UR - http://www.scopus.com/inward/record.url?scp=44349194348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44349194348&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.77.052331

DO - 10.1103/PhysRevA.77.052331

M3 - Article

AN - SCOPUS:44349194348

VL - 77

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 5

M1 - 052331

ER -