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

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