Summary

In this chapter, we have introduced the quantum circuit model and the main concepts that it relies on: qubits, gates, and measurements. We have started by studying the most humble circuits, those that only have one or two qubits, but we have used our experience with them to grow all the way up to multi-qubit systems. In the process, we have discovered some powerful properties, such as superposition and entanglement, and we have mastered the mathematics — mainly some linear algebra — needed to work with them.

These notions will be extremely valuable to us, because they make up the language in which we will be describing the quantum algorithms for machine learning and optimization that we will study in the rest of the book. Soon, all the pieces will come together to form a beautiful structure. And we will be able to appreciate it and understand it fully because of the solid foundations that we have acquired by now.

In the next chapter, we will start applying all that we have learned by implementing and running quantum circuits on quantum simulators and on actual quantum computers. We don't know about you, but we are pretty excited!