11 Facts About Hadamard transform

Hadamard transform is an example of a generalized class of Fourier transforms.

Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms, and is in fact equivalent to a multidimensional DFT of size.

Hadamard transform is in fact equivalent to a multidimensional DFT of size.

In quantum computing, the Hadamard transform gate is a one-qubit rotation, mapping the qubit-basis states and to two superposition states with equal weight of the computational basis states and.

However, if the Hadamard transform gate is applied twice in succession, then the final state is always the same as the initial state.

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Computing the quantum Hadamard transform is simply the application of a Hadamard gate to each qubit individually because of the tensor product structure of the Hadamard transform.

Hadamard transform can be used to estimate phylogenetic trees from molecular data.

The invertible nature of the phylogenetic Hadamard transform allows the calculation of site likelihoods from a tree topology vector, allowing one to use the Hadamard transform for maximum likelihood estimation of phylogenetic trees.

However, the invertible nature of the phylogenetic Hadamard transform does provide an elegant tool for mathematic phylogenetics.

Hadamard transform is used in data encryption, as well as many signal processing and data compression algorithms, such as JPEG XR and MPEG-4 AVC.

The Hadamard transform is applied in experimental techniques such as NMR, mass spectrometry and crystallography.