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Discrete time quantum walks are known to be universal for quantumcomputation. This has been proven by showing that they can simulate a universalquantum gate set. In this paper, we examine computation by quantum walks interms of language acceptance, and present two ways in which discrete timequantum walks can accept some languages with certainty. These walks can takequantum as well as classical inputs, and we show that when the input isquantum, the walks can also be interpreted as performing the task of quantumstate discrimination.

The expressive power of quantum walks in terms of language acceptance