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This Demonstration explores the properties of one-, two-, and three-qubit quantum logic gates.

It is interesting to note that fundamental properties of the Hadamard operator

can be expressed in a neat form, using trigonometric functions of the angle

. Its eigenvectors and eigenvalues are

. A Hadamard gate can be represented in exponential form as

and its square root takes the form

. Here

and

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Quantum Logic Gates: Roots, Exponents, and Eigensystems