quantum gate directory
Hadamard
Symbol
$H$
Description:
Maps computational basis states to equal superpositions and swaps the $X$ and $Z$ bases.
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.HGate
|
| PennyLane |
pennylane.Hadamard
|
| Cirq |
cirq.H
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The Hadamard gate creates and removes superposition by mapping $|0\rangle \mapsto |+\rangle$ and $|1\rangle \mapsto |-\rangle$.
$$ H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} $$
Properties
- Self-inverse and Hermitian: $H^\dagger = H$.
- Conjugates Pauli operators: $H X H = Z$ and $H Z H = X$.
- Real and symmetric.
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