Deutsch's Universal Quantum Computer:

In 1985 David Deutsch published his seminal paper Quantum theory, the Church-Turing principle and the universal quantum computer [6]. In this paper Deutsch defined a quantum generalization of the classical Turing machine, showed that all Turing computable functions are also computable by his universal quantum computer, and exhibited a task that his universal quantum computer is more efficient for than any classical restriction of it [6].

Following this paper, researchers identified several toy problems that a quantum computer is exponentially faster for than a classical Turing machine [5] [3]. Unfortunately, these were all contrived problems with no practical application. While the potential for exponential speedup fostered great curiosity, the study of quantum computing remained primarily academic.