Experimental revival of an unknown state from the past in quantum walks.

The physical process in the macroscopic world unfolds along a single time direction, while the evolution of a quantum system is reversible in principle. How to recover a quantum system to its past state is a complex issue of both fundamental and practical interests. In this article, we experimentally demonstrate a novel method for recovering the state in quantum walks (QWs), also known as full-state revival. Moreover, we observe two other important phenomena in QWs, recurrence and periodicity, via simplifying and repeatedly implementing the scheme, respectively. Our experiments show that obtaining these phenomena requires neither any information of the initial state nor full information of the coin operations. Our work sheds new light on quantum state engineering and recovery, and the initialization of quantum devices based on QWs.