Identity Gate

Last updated Jun 23, 2022

• Type atom
• Status unfinished
• On quantum computing

The identity gate does nothing to the bit, i.e. $0$ remains $0$ and $1$ remains $1$. The identity gate is sometimes depicted by a triangle in a circuit diagram, but often, we omit the triangle and just draw a longer wire. Chapter 1 - Classical Information and Computation > ^b3cedc

• In case of Quantum Computing, the identity gate turns $\ket 0$ into $\ket 0$ and $\ket 1$ into $\ket 1$, hence it does nothing: $$\displaylines{
  I\ket0 = \ket 0, \newline
  I\ket1 = \ket 1.
  }$$ Chapter 2 - One Quantum Bit > ^736c4b #to/embed
• It’s Matrix representation is: $$I = \begin{pmatrix}1 & 0 \\ 0 & 1 \end{pmatrix}.$$

• wongIntroductionClassicalQuantum