9.6 Quantum gates and operations

We’ve already encountered qubits twice in this book, first in the introductory section 1.11, and then again in section 5.8 where we explored quantum randomness. The remainder of this chapter expands those discussions and places them in the larger quantum computing context.

Though I’ll discuss and use qubits here, I will not repeat the mathematical foundation of complex numbers, probability, and linear algebra from other texts. [DWQ]

9.6.1 Introduction to 1-qubit gates

We represent the value or state of a qubit as two complex numbers (a, b) such that

|a|² + |b|² = 1 .

For example, we might have a = 1 and b = 0, or the other way around. These are important cases, and we have special names for them. (1, 0) is |0⟩, pronounced “ket-0,” and (0, 1) is |1⟩, pronounced “ket-1.”

If you are familiar...