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If The Matrix really existed, it would probably have to be a quantum simulator. The fictional computer in that story can create virtual worlds indistinguishable from the real one and project them into people’s minds. But the real world includes quantum phenomena, something ordinary computers can’t fully simulate.

Now physicists have created a rudimentary prototype of a machine that simulates quantum phenomena using quantum physics, rather than using data kept in a classical computer. While the new device can't make people fly like the Matrix does, it demonstrates a technique that could enable physicists to create, in the virtual world, materials that don't yet exist in nature and perhaps figure out how to build, in the real world, superconductors that work at room temperature, for example.

Source: http://www.sciencenews.org/view/generic/id/34497/title/Building_The_Matrix