Adiabatic quantum computation is equivalent to standard quantum computation

Dorit Aharonov, Wim Van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, Oded Regev

Research output: Contribution to journalArticle

Abstract

Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.

Original languageEnglish (US)
Pages (from-to)166-194
Number of pages29
JournalSIAM Journal on Computing
Volume37
Issue number1
DOIs
StatePublished - 2007

Fingerprint

Quantum computers
Quantum Computation
Quantum Algorithms
Spectral Gap
Sparse matrix
Eigenvalues and eigenfunctions
Computer science
Eigenvector
Nearest Neighbor
Open Problems
Computer Science
Physics
Equivalence
Model
Grid
Imply
Unknown
Interaction
Standards
Simulation

Keywords

  • Adiabatic computation
  • Nearest neighbor interactions
  • Quantum computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Adiabatic quantum computation is equivalent to standard quantum computation. / Aharonov, Dorit; Van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded.

In: SIAM Journal on Computing, Vol. 37, No. 1, 2007, p. 166-194.

Research output: Contribution to journalArticle

Aharonov, Dorit ; Van Dam, Wim ; Kempe, Julia ; Landau, Zeph ; Lloyd, Seth ; Regev, Oded. / Adiabatic quantum computation is equivalent to standard quantum computation. In: SIAM Journal on Computing. 2007 ; Vol. 37, No. 1. pp. 166-194.
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