- Home
- Projects and blogs
- Quantum computing
- The Hadamard gate

The Hadamard gate is a type of single-qubit quantum gate—a basic operation that can be applied to a qubit. Like all quantum gates, the Hadamard gate is a unitary transformation on a Hilbert space, and it is defined as follows:

$H=[2 1 2 1 2 1 −2 1 ].$

When acted on either of the basis states, the Hadamard gate produces an even superposition of $∣0⟩$ and $∣1⟩$:

$H∣0⟩=[2 1 2 1 2 1 −2 1 ][10 ]=[2 1 2 1 ],$

$H∣1⟩=[2 1 2 1 2 1 −2 1 ][01 ]=[2 1 −2 1 ],$

with either of the measurement outcomes being equally likely.

Additionally, the Hadamard operation is its own inverse; applying it twice returns a qubit to its original state:

$HH=[2 1 2 1 2 1 −2 1 ][2 1 2 1 2 1 −2 1 ]=[10 01 ]=I,$

where $I$ is the identity matrix.

- Quantum Random Number Generator - Generate random numbers using quantum computing.
- Bloch Sphere - Visualize qubits on a Bloch sphere.
- Say "Hello, World!" with Q# - Creating a simple Q# console application.
- Quantum Gates Quiz - Test your knowledge of quantum logic gates.

Made by Anton Vasetenkov.

If you want to say hi, you can reach me on LinkedIn or via email. If you like my work, you can support me by buying me a coffee.