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Majorization in Quantum Adiabatic Algorithms

Zhaohui Wei·Zhengfeng Ji·Mingsheng Ying
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Abstract

The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to appear universally in quantum adiabatic algorithms. In this paper, a rigorous analysis of the majorization arrow in a special class of quantum adiabatic algorithms is carried out. In particular, we prove that for any adiabatic algorithm of this class, step-by-step majorization of the ground state holds exactly. For the actual state, we show that step-by-step majorization holds approximately, and furthermore that the longer the running time of the algorithm, the better the approximation.

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Zhaohui Wei, Zhengfeng Ji, Mingsheng Ying. 2006-06-01. Majorization in Quantum Adiabatic Algorithms. https://doi.org/10.1103/physreva.74.042320

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