Introducing multiple quantum bits
Multiple qubit operations will allow us to implement more complex quantum algorithms in the upcoming chapters. Dealing with multiple qubits is a core requirement in quantum computing because in most cases, the information can only be encoded by the use of many qubits. Multiple qubits also bring flexibility in computation as we can perform quantum operations more conveniently.
You studied some of the basics of tensor products in Chapter 1, Essential Mathematics and Algorithmic Thinking, which will now help you to appreciate the nature of multiple qubits in a quantum computing environment. As we know, single qubits are denoted as |0>, |1>, or any generic state . To denote two qubits, we use the notation |00>, |11>, or any generic state, such as . We can have two different quantum subsystems, each having their own vector spaces. Their interactions can be denoted by the addition and scalar multiplication of the vector elements, which we...