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Trapped Ion Quantum Computing

Effect of Local Minima on Adiabatic Quantum Optimization

arXiv
Authors: M. H. S. Amin

Year

2007

Paper ID

49168

Status

Preprint

Abstract Read

~2 min

Abstract Words

94

Citations

N/A

Abstract

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

Why This Paper Matters

  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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  • We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0709.0528 [2] arXiv https://arxiv.org/abs/0709.0528 [3] Publisher https://arxiv.org/abs/0709.0528

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