An introduction to the geometrical formulation of quantum complexity

In this talk, I will provide an overview of the idea of quantum complexity, which measures the minimum number of simple operations required to achieve a given task. I will particularly talk about the geometrical formulation of complexity, developed by Nielsen and his collaborators, which provides an elegant way of identifying the optimal quantum circuit that can construct the desired unitary transformation with geodesics in the space of unitaries equipped with a suitable metric. Finally, using the harmonic oscillator as an example, I will show how to compute the complexity of specific operators.