2.3 How to transform a qubit state
In a classical computer, the state of bits is transformed using logic gates. For example, the negation or NOT gate is a one-bit gate that transforms a bit in state 0 to a bit in state 1, and vice-versa. These logic gates are the basic ingredients that are then used to construct classical algorithms. In fact, as you probably know, the chip in your computer is nothing more than a vast mesh of interconnected logic gates!
In quantum computing, we don’t use logic gates, but quantum gates. These—together with measurement operations—are the building blocks that enable us to construct any quantum algorithm. What are these quantum gates and how can we use them? Let’s find out.
2.3.1 Quantum gates
From a mathematical point of view, a quantum gate is any unitary operator acting on the vector space of states (in the case of a one-qubit system, ℂ2). In case you don’t remember (we also discuss this in Appendix 15...
