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With the exception of cryptography applications like Shor's algorithm and quantum key distribution, I think engineering 'killer-apps' are not the norm for quantum computing, and nobody expects them to be. As such, quantum walks are a natural generalization of random walks and thus worth studying in their own right. However, to avoid side-stepping any longer, ...

Quantum statistics are also recreated in Maximal Entropy Random Walk, which has lots of known applications: "MERW is used in various fields of science. A direct application is choosing probabilities to maximize transmission rate through a constrained channel, analogously to Fibonacci coding. Its properties also made it useful for example in analysis of ...