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arXiv · 1410.3562

Theorem on the existence of a nonzero energy gap in adiabatic quantum computation

Da-Jian Zhang·Xiao-Dong Yu·D. M. Tong
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Abstract

Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and excited states. However, it is difficult to ascertain the exact value of the energy gap. In this paper, we put forward a theorem on the existence of nonzero energy gap for the Hamiltonians used in adiabatic quantum computation. It can help to effectively identify a large class of the Hamiltonians without energy-level crossing between the ground and excited states.

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Da-Jian Zhang, Xiao-Dong Yu, D. M. Tong. 2014-10-14. Theorem on the existence of a nonzero energy gap in adiabatic quantum computation. https://doi.org/10.1103/physreva.90.042321

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