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- 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.

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- Quantum Gates Quiz - Test your knowledge of quantum logic gates.
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- Q# Editor - Edit Q# files online.
- Awesome quantum computing - A curated list of awesome resources on quantum computing.
- Quantum Computing Crossword - A daily crossword puzzle about quantum computing.
- Quantum computing pronunciation guide - A pronunciation guide for quantum computing terms.

Made by Anton Vasetenkov.

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