Coherence evolution of three-state quantum walk on lattice

Abstract

Coherence is crucial in quantum information processing, and quantum walk provide an excellent model for studying fundamental quantum theory and quantum algorithm design. The coherence of the initial state, system boundaries, coin operators, and evolution time are all relevant factors in the evolution of coherence systems. Using l1 norm as the coherence measure, the evolution characteristics of coherence in the three-state quantum walk with boundaries in a 2D lattice were investigated, and the effects of broken links, phase damping, amplitude damping, and unitary noise on the coherence of the three-state quantum walk were analyzed. The results show that the boundaries suppress the growth of coherence of a single-point initial state of the entire system, but does not affect the coherence of equal-weight superposition states. Small noise can slightly enhance the coherence of the entire system and position subsystems for broken links and unitary noise, while larger noise suppresses the growth of coherence.