Apart from the others already mentioned, one very recent example of a breakthrough that has both intrinsic and applied value is the June 2012 paper by Stephen Jordan, Keith Lee, John Preskill on Quantum algorithms for Quantum Field theories.
Intrinsic value - The paper has shown that simple quantum field theories can be simulated efficiently on a quantum computer, thus paving the way towards a quantum algorithm for simulating the Standard Model of particle physics. 'Such an algorithm would establish that, except for quantum-gravity effects, the standard quantum circuit model sufﬁces to capture completely the computational power of our universe'
Possible applications - The ability to efficiently simulate field theories would give us the power to analyze systems that have evaded physicists for many years, ranging from very high-energy particle collisions and quantum many-body systems to the early universe itself.
- The paper was published in Science
- Science-Mag perspectives on the paper can be found here.
- The full-text extended pre-print can be found on Arxiv.