Evolution process and properties of wave-particle quantum walk(QW)are studied by theoretical calculation and quantum simulator's simulation.Quantum control can contribute to the realization of QWs in quantum wave-particle superposition state with a relative phase between walkers.The post-selection operation is used to realize the continuous transitions of QW from the state of waves with multi-path coherence to the state of particles without coherence in two different ways:coherence and mixing.Due to quantum interference,there are essential differences between coherence and mixing,and their specific features are characterized by position variance.We also demonstrate the coherent wave-particle QWs in the real quantum simulator.When the walker is in the wave-particle coherent state,two completely different properties can be observed simultaneously through one measurement.By adjusting the relative phase in the wave-particle coherent state,the diffusion rate of the walker can be controlled.
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