We implement several quantum algorithms in real five-qubit superconducting quantum processor IBMqx4 to perform quantum computation of the dynamics of spin-1/2 particles interacting directly and indirectly through the boson field. Particularly, we focus on effects arising due to the presence of entanglement in the initial state of the system. The dynamics is implemented in a digital way using Trotter expansion of evolution operator. Our results demonstrate that dynamics in our modeling based on real device is governed by quantum interference effects being highly sensitive to phase parameters of the initial state. We also discuss limitations of our approach due to the device imperfection as well as possible scaling towards larger systems.
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