Abstract
This chapter presents a series of mathematical tools and algorithmic techniques for analysis of quantum programs with classical control. We start from examining the behavior of quantum while-loops, including termination and average running time. An example is given to compute the average running time of a quantum walk on an n-circle. The studies of quantum while-loops lead us to define quantum Markov chains as a general semantic model of quantum programs. It is shown that termination analysis of quantum programs can be reduced to the reachability problem of quantum Markov chains. The second part of this chapter is then devoted to developing algorithms for reachability analysis of quantum Markov chains. As a crucial mathematical tool for this purpose, a new theory of quantum graphs is introduced.
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