TY - JOUR
AB - 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. © 2006 The American Physical Society.
AU - Wei, Z
AU - Ji, Z
AU - Ying, M
DA - 2006/10/25
DO - 10.1103/PhysRevA.74.042320
JO - Physical Review A - Atomic, Molecular, and Optical Physics
PY - 2006/10/25
TI - Majorization in quantum adiabatic algorithms
VL - 74
Y1 - 2006/10/25
Y2 - 2019/07/21
ER -