  In this paper, we consider the secret-string-learning problem in the
teacher-student setting: the teacher has a secret string $s\in
{{\{0,1\}}^{n}}$, and the student wants to learn the secret $s$ by
question-answer interactions with the teacher, where at each time, the student
can ask the teacher with a pair
  $(x, q) \in {{\{0,1\}}^{n}}\times\{0,1,\cdots, n-1\}$ and the teacher returns
a bit given by the oracle $f_{s}(x,q)$ that indicates whether the length of the
longest common prefix of $s$ and $x$ is greater than $q$ or not. Our
contributions are as follows.
  (i) We prove that any classical deterministic algorithm needs at least $n$
queries to the oracle $f_{s}$ to learn the $n$-bit secret string $s$ in both
the worst case and the average case, and also present an optimal classical
deterministic algorithm learning any $s$ using $n$ queries.
  (ii) We obtain a quantum algorithm learning the $n$-bit secret string $s$
with certainty using $\left\lceil n/2\right\rceil$ queries to the oracle $f_s$,
thus proving a double speedup over classical counterparts.
  (iii) Experimental demonstrations of our quantum algorithm on the IBM cloud
quantum computer are presented, with average success probabilities of $85.3\%$
and $82.5\%$ for all cases with $n=2$ and $n=3$ , respectively.
