Dirac Notation (Bra‐Ket Notation) - RPIQuantumComputing/QuantumCircuits GitHub Wiki

History

Bra-ket notation was initially created by the famous physicist Paul Dirac for his 1939 publication A New Notation For Quantum Mechanics, in which is was introduced to serve an easier way to write quantum mechanical expressions. Although most commonly used in physics, it can be used in mathematics to denote abstract vectors and linear functionals.

Description

Bra-Ket, otherwise known as Dirac notation is a form of notation commonly used to describe quantum states. There are two components to bra ket notation as the name might imply. These are as follows...

• Bra: A bra is written like so $\langle f|$. As for what it means, the bra describes a linear mapping, $f: V \rightarrow C$. This means that each vector in $V$ is mapped to a number in the complex plane $C$.

• Ket: A ket takes the form $|v \rangle$ and describes a vector $v$ in a complex vector space $V$. In quantum physics it is used to represent the quantum state of a system.

When the two are combined the following term is the result, $\langle f| v\rangle$. This expression means that the linear mapping $f$ is acting on the vector $v$.