Quantum walk as generalized evolution and measurement device

Abstract

We show that arbitrary quantum evolution, both unitary and non-unitary ones, can be efficiently realized via one-dimensional quantum walk. This is done based on the equivalence between quantum evolution and positive-operated valued measurements, and an algorithm of properly controlling one-dimensional discrete-time quantum walk to realize arbitrary positive-operated valued measurements. Furthermore, our method based on one-dimensional quantum walk can be easily generalized to other platforms Our method enriches technics for quantum information processes, and the applications of quantum walk.