  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.
