Quantum walk in (1+1)-dimensional spacetime for Majorana dynamics with high order approximation in NISQ

In this study, we show that quantum walk can describe a Majorana fermion when the coin operator constrained by Lorentz covariance and the initial state satisfies the Majorana condition. The time evolution of a Majorana fermion is demonstrated with the numerical simulations and experimentally runs on a real quantum device provided by IBM Quantum System. To reduce errors due to approximation, we proposed a new efficient way to achieve second order accuracy in the near-term quantum computer without increase the complexity of quantum gate circuitry compared with the first order approximation. We show that rest Majorana fermion (expectation value of momentum is zero) can be well defined and its behavior depends more sensitively on the accuracy of the approximation than a Dirac particle due to the stringent constraints of Majorana condition.