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In [Wolfram 1982; Wolfram 1983; Wolfram 2002], the backtracking ofone-dimensional cellular automata is to find out which of the 2n possibleinitial configurations of width n evolve to a specific configuration. In thispaper, in one-dimensional cellular automata for a specific configuration ofwidth n, its unique initial configuration can be found by mean of the proposedquantum algorithm with polynomial quantum gates, polynomial quantum bits andthe successful probability that is the same as that of Shor's quantumorder-finding algorithm in [Shor 1994].

Quantum Algorithms of Solving the Backtracking of One-dimensional Cellular Automata