This function applies the Hadamard transformation to a single qubit. It will basically flip the qubit halfway instead of all the way. The Haramard transform is used in data encryption, as well as signal processing algorithms such as JPEG XR and MPEG-4 Audio Video Codec. In video compression it is usually used in order to for the sum of absolute transformed differences. The Hadamard transformation is also used in scientific methods such as mass spectroscopy and crystallography among others.

Currently, the Hadamard function is defined as: