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