constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
quantum algorithms:
In qbit-based quantum computation, by the Pauli gates one means the linear basis of quantum gates on single qbits, hence on the 2-dimensional Hilbert spaces $QBit \simeq \mathbb{C}^2$, which, in terms of the canonical quantum measurement-basis $\mathbb{C}^2 \simeq Span\big( \{ \vert 0 \rangle ,\, \vert 1 \rangle\} \big)$, are given by the Pauli matrices.
Explicitly this means that (in the conentional normalization) the:
Pauli-X gate (or quantum NOT gate) is given by the matrix
Pauli-Y gate is given by the matrix
Pauli-Z gate is given by the matrix
The Hadamard gate transforms the eigenstates $\vert 0 \rangle$, $\vert 1 \rangle$ of the Pauli Z-gate into those $\propto \vert 0 \rangle \pm \vert 1 \rangle$ of the Pauli-X gate, a relation that is elaborated on by the correspondingly named ZX-calculus.
For example:
Created on March 7, 2023 at 15:10:18. See the history of this page for a list of all contributions to it.