Observing Majorana fermion dynamic properties on a NISQ computer

Majorana particles are of particular interest due to their profound property of being their own anti-particles and potential applications for quantum computers. However, studying the dynamics of Majorana particles experimentally has proven to be challenging, with many unanswered questions about their behaviors. In this paper, we demonstrate that an improved discrete-time quantum walks (DTQW) on a Noisy Intermediate-Scale Quantum (NISQ) computer can be used to construct a well-defined Majorana fermion. Through this approach, we can observe the behaviors of Majorana particle propagation both in (1 + 1)- and (3 + 1)-dimensions. A counter-intuitive dynamic behavior of the non-vanishing expectation value of velocity and position with zero expectation value of momentum from the superposition of positive and negative energy solution is observed for the first time in NISQ. Our findings provide a promising avenue for experimentally studying the dynamical properties of Majorana particles.