Defining a quantum active particle using a non-unitary quantum walk

The main aim of the present paper is to define an active matter in a quantum framework and investigate difference and commonalities of quantum and classical active matters. We here propose a truly deterministic quantum active-matter model with a non-unitary quantum walk as minimal models of quantum active matter. We aim to reproduce similar results that Schweitzer et al. (1998) obtained with their classical active Brownian particle. With our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a non-trivial way as we increase the non-Hermiticity parameter, which is similar to the classical active Brownian particle (Schweitzer et al., 1998). Meanwhile, we also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state and excited state both in one and two dimensions.