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The Klein Gordon equation was the first attempt at unifying specialrelativity and quantum mechanics. While initially discarded this equation of"many fathers" can be used in understanding spinless particles thatconsequently led to the discovery of pions and other subatomic particles. Theequation leads to the development of Dirac equation and hence quantum fieldtheory. It shows interesting quantum relativistic phenomena like Klein Paradoxand "Zitterbewegung", a rapid vibrating movement of quantum relativisticparticles. The simulation of such quantum equations initially motivated Feynmanto propose the idea of quantum computation. While many such simulations havebeen done till date in various physical setups, this is the first time adigital quantum simulation of Klein Gordon equation is proposed on IBM'squantum computer. Here we simulate the time-dependent Klein Gordon equation ina barrier potential and clearly observe the tunnelling of the particle andanti-particle through a strong potential claiming Klein Paradox. The simulationtechnique used here inspires the quantum computing community for furtherstudying Klein Gordon equation and applying it to more complicated quantummechanical systems.

Quantum Simulation of Klein Gordon Equation and Observation of Klein Paradox in IBM Quantum Computer