In the second step, we will tackle the matrix squaring procedure, discretized,

and in a homogeneous space. It will allow you to determine pi(x)

now without having to resort to something which is close to the Schrödinger evolution,

that is, in the iteration of the algorithm, by decreasing the temperature.

Finally, in the third step, we will have in fun in firing up the naive Quantum Monte Carlo algorithm,

which allows you in a third way to determine

pi(x), now by sampling in a histogram the position x of the particle.

All in all, for those of you who already know Quantum Mechanics,

but also for those of you who do not know anything about Quantum Mechanics,

you will learn three different recipes to study the evolution of such systems.