Timeline of quantum computing
From Academic Kids

1970  Stephen Wiesner invents conjugate coding.
1973  Alexander Holevo publishes a paper showing that n qubits cannot carry more than n classical bits of information.
1976  Polish mathematical physicist Roman Ingarden, in one of the first attempts at creating a quantum information theory, shows that Shannon information theory cannot directly be generalized to the quantum case, but rather that it is possible to construct a quantum information theory which is a generalization of Shannon's theory.
1981  Richard Feynman in his talk at the First Conference on the Physics of Computation, held at MIT, observed that it appeared to be impossible in general to simulate a evolution of a quantum system on a classical computer in an efficient way. However, instead of viewing this intractability as an obstacle, Feynman regarded it as an opportunity. He pointed out that if it requires that much computation to work out what will happen in a multiparticle interference experiment, then the very act of setting up such an experiment and measuring the outcome is equivalent to performing a complex computation.
1984  Charles Bennett and Gilles Brassard employ Wiesner's conjugate coding for distribution of cryptographic keys.
1985  David Deutsch, at the University of Oxford, described the first universal quantum computer. Just as a universal Turing machine can simulate any other Turing machine efficiently, so the universal quantum computer is able to simulate any other quantum computer with at most a polynomial slowdown.
1991  Artur Ekert invents entanglement based secure communication.
1993  Dan Simon, at Université de Montréal, invented an oracle problem for which quantum computer would be exponentially faster than conventional computer. This algorithm introduced the main ideas which were then developed in Peter Shor's factoring algorithm.
1994  Peter Shor, at AT&T's Bell Labs in New Jersey, discovered a remarkable algorithm. It allowed a quantum computer to factor large integers quickly. It solved both the factoring problem and the discrete log problem. Shor's algorithm could theoretically break many of the cryptosystems in use today. Its invention sparked a tremendous interest in quantum computers, even outside the physics community.
1995  Shor proposed the first scheme for quantum error correction. This is an approach to making quantum computers that can compute with large numbers of qubits for long periods of time. Errors are always introduced by the environment, but quantum error correction might be able to overcome those errors. This could be a key technology for building largescale quantum computers that work. These early proposals had a number of limitations. They could correct for some errors, but not errors that occur during the correction process itself. A number of improvements have been suggested, and active research on this continues. An alternative to quantum error correction has been found. Instead of actively correcting the errors induced by the interaction with the environment, special states that are immune to the errors can be used. This approach, known as decoherence free subspaces, assumes that there is some symmetry in the computerenvironment interaction.
1996  Lov Grover, at Bell Labs, invented the quantum database search algorithm. The quadratic speedup isn't as dramatic as the speedup for factoring, discrete logs, or physics simulations. However, the algorithm can be applied to a much wider variety of problems. Any problem that had to be solved by random, bruteforce search, could now have a quadratic speedup.
1997  David Cory, A.F. Fahmy and Timothy Havel, and at the same time Neil Gershenfeld and Isaac Chuang at MIT published the first papers on quantum computers based on bulk spin resonance, or thermal ensembles. The computer is actually a single, small molecule, which stores qubits in the spin of its protons and neutrons. Trillions of trillions of these can float in a cup of water. That cup is placed in a nuclear magnetic resonance machine, similar to the magnetic resonance imaging machines used in hospitals. This roomtemperature (thermal) collection of molecules (ensemble) has massive amounts of redundancy, which allows it to maintain coherence for thousands of seconds, much better than many other proposed systems.
1998  First working 2qubit NMR computer demonstrated at University of California, Berkeley.
1999  First working 3qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of Grover's algorithm.
2000  First working 5qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of order finding (part of Shor's algorithm).
2001  First working 7qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of Shor's algorithm. The number 15 was factored using 10^{18} identical molecules, each containing 7 atoms.