Quantum algorithm to solve function inversion with time-space trade-off

In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time-space trade-off in this paper. The details are as follows. Let function f (x) = y have k solutions, where x is an element of {0, 1}(n), y is an element of{0, 1}(m) for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f (x) with successful probability 1 - (1 - k/2(n))(L) for L is an element of Z(+). The space complexity of proposed quantum iterative algorithm is O( Ln), where L is the number of iterations. The paper concludes that, via using time-space trade-off strategy, we improve the successful probability of algorithm.