# Spectral Gap Amplification

@article{Somma2011SpectralGA,
title={Spectral Gap Amplification},
author={Rolando D. Somma and Sergio Boixo},
journal={SIAM J. Comput.},
year={2011},
volume={42},
pages={593-610}
}
• Published 11 October 2011
• Physics
• SIAM J. Comput.
Many problems can be solved by preparing a specific eigenstate of some Hamiltonian $H$. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of $H$ for that eigenstate and the cost of evolving with $H$ for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian $H'$ with the same eigenstate as $H$ but a bigger spectral gap, requiring that constant-time evolutions with $H'$ and $H$ are implemented with nearly the same…

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