- Anton V.
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- 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.

- Bloch Sphere - Visualize qubits on a Bloch sphere.
- Quantum Computing Crossword - A daily crossword puzzle about quantum computing.
- Quantum Random Number Generator - Generate random numbers using quantum computing.
- Quantum Gates Quiz - Test your knowledge of quantum logic gates.
- Say "Hello, World!" with Q# - Creating a simple Q# console application.
- Q# Editor - Edit Q# files online.

Made by Anton Vasetenkov.

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