Solving linear equations with quantum computers

In the video, Menno Veldhorst discussed that the solution vector of the system is not an output of the HHL algorithm. In other words, we need to “ask a quantum mechanical question” to this output vector to obtain some information about the solution of our problem. This way, quantum algorithms are significantly different from classical algorithms, where we immediately get the answer to our problem.

In fact, this is true for many quantum algorithms in general. So what do you think is the main challenge in constructing quantum algorithms?

One big challenge is to design an algorithm that actually solves the problem you are looking forward to solve. In the end, most algorithms aim to prepare a superposition of states such that when you measure you have a high probability of measuring what you want. This means the steps of the algorithm need to ensure a high probability of the wanted state, without you knowing what this state is like in advance.