Matrix representation of bits and gates

For an inkling of the way matrices work in computer logic, we introduce two new ways to represent bits:

• In Dirac notation, the zero bit is |0⟩, and the one bit is |1⟩.

The | ⟩ combination of characters is called a ket.

• In vector notation, the zero bit is , and the one bit is .

These new ways to represent bits may seem cumbersome and redundant, but they’re really very helpful. If you like, think of the numbers in a vector as amounts ranging from zero to one. A vector’s top entry is an amount of zero-ness and the vector’s bottom entry is an amount of one-ness.

Figure 1.16 – The correspondence between vector notation and Dirac notation

This business about all zero-ness and all one-ness will make more sense when you read about qubits in the next chapter.

Disclaimer

Most authors reserve kets and vectors for qubits (quantum bits). For...