Adiabatic quantum computation with a one-dimensional projector Hamiltonian

Tulsi, Avatar (2009) Adiabatic quantum computation with a one-dimensional projector Hamiltonian. In: Physical Review A, 80 (5).

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Abstract

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

Item Type:	Journal Article
Publication:	Physical Review A
Publisher:	The American Physical Society
Additional Information:	copyright of this article belongs to The American Physical Society.
Keywords:	ground states;Hilbert spaces;quantum computing.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	09 Jan 2010 09:39
Last Modified:	19 Sep 2010 05:54
URI:	http://eprints.iisc.ac.in/id/eprint/25322

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