State Symbols

Let’s start by thinking about two wires in a traditional computer. The voltage differences between wires in the computer are used for several purposes: to bring information to gates for processing and to indicate where data should come from and go. Each wire has two states (or conditions): The voltage is “high” $V_{high}$ or the voltage is “low” $V_{low}$. Because there are just two states, this is a binary system.

We can represent those two voltage states by the symbols $\ket{ V_{high}}$ and $\ket{V_{low}}$. Each symbol consists of a vertical line on the left and an angle bracket on the right. You should think of the combination $\ket{}$ as a container. The contents of the container are names that label the two possible states. So, we could have $\ket{On}$ and $\ket{Off}$ states or $\ket{True}$ and $\ket{False}$ states or $\ket{Awake}$ and $\ket{Asleep}$ states, and so on. These $\ket{}$ symbols are widely used in quantum computing to represent quantum states. You might think of state symbols as a form of emoji ☺. In and of themselves, the labels or names have no numerical or even direct physical meaning.

This symbol is part of what is called Dirac notation, invented by Paul Dirac, an English physicist who lived from 1902 to 1984, who was one of the pioneers in quantum mechanics. He developed this notation in 1939, about 13 years after the birth of quantum mechanics, to clarify the procedures of quantum mechanics. QC and QIS make wide use of Dirac notation.