In the second video, Professor Bertels emphasizes that we should repeat our quantum algorithm many times since we rely on quantum measurements. Why is that? Suppose we increase our number of measurements by a factor of 2, can we “trust” our outcome twice as good as well? Why (not)?
Each time a measurement is performed, the wavefunction collapses to a result and the rest of the information is lost. If we only measured once, we wouldn't be able to figure out what the amplitudes of the wavefunction looked like. We can only do so if we estimate them based on the probabilities of measuring one result or another.
Whether we can trust each outcome or not does not linearly depend on the number of measurements performed. Compare the situations in which you measure only once and twice. Are you really gaining double amount of information?