Cool study, but some seriously bad explanation in the article.
Technology, helped by colleagues from Switzerland and the U.S inverted the flow of time for a quantum computer and an electron for a fraction of a second, contradicting the second law of thermodynamics, which says that a natural process runs only in one sense and is not reversible.
Neither of the underlined statements is correct. This does not contradict the 2nd law, and many natural processes are reversible. What the 2nd law says is that processes are (usually vastly) more likely to proceed in the direction that increases entropy. But there are also reversible processes that do not change the entropy. For example, the expansion of a universe filled with photons. A more down-to-earth example is the Carnot cycle, which is built from four different reversible processes, two of which do not change the entropy and the other two which do by extracting heat and doing work. It is also the most efficient way possible to extract useful energy from a thermodynamic system.
What they did here with the quantum computer is reverse the evolution of the system by "a time reversal". For a classical example we can imagine a pool table. Someone makes a good break, and immediately before the balls come to rest, we imagine perfectly reversing all of their velocities. In practice this is obviously difficult to do, but it is simple enough in a computer simulation. What happens is all the balls perfectly retrace their paths, come together and reform the rack, transferring all their momenta to the cue ball which then flies back to the stick.
What does the 2nd law have to say for this situation of reversing the break in pool? After the break, the balls move to occupy more possible places in space on the table, as well as in momentum space
(the momentum transfers from one ball to many, with each ball having a wide range of possible values of momentum after the collision). Since many more possibilities exist after the break, the entropy increases, and therefore the 2nd law tells us this process should not be easily reversible. We should not expect it to naturally happen in reverse, and by observation, it doesn't.
For a quantum system, the situation is more complicated. The evolution is described by the Schrödinger equation, for which the results are probabilistic (we can't know exactly where an electron will be found in a measurement for example, but rather a set of probabilities for finding it at different locations), and the Schrödinger equation describes how those probabilities change over time.
For some simple case, we might imagine an electron confined inside a box. Classically, we would image the electron as a particle bouncing regularly back and forth. But quantum mechanically, it is a wave. If we measure where the electron is, the wave immediately collapses to that location, indicating "the electron is right here". But then it proceeds to spread out again according to the Schrödinger equation. Another measurement made very quickly afterward may find the electron in nearly the same place, but after a lot of time it could be anywhere in the box, again with probability being related to the shape of the wave. Furthermore, the greater the uncertainty in the momentum of the electron, the faster the wave will spread out, and likewise so too will the spread of uncertainty in where the next measurement will locate the electron.
With the evolution of qubits in a quantum computer, the time reversal and subsequent measurements must occur very quickly, or else that spread of uncertainty will result in the system not returning to its original state. This is why there is not a 100% success rate, and lower for more qubits.