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An Introduction To Orthonormal Bases

An essential lesson on Orthonormal bases that help represent the state of Quantum systems.

Dr. Ashish Bamania
Into Quantum

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A photograph taken during a lecture by Richard Feynman, one of the most significant physicists of the 20th century, who sparked the idea of Quantum computers, which leverage quantum mechanics to perform computations. (Image from Wikimedia Commons)

I have been writing a Quantum Computing publication called Into Quantum, and here is one of the fundamental lessons you need to learn in Quantum mechanics before understanding how Quantum computers work.

In case you missed the previous lessons on Linear Algebra required to understand this lesson, here they are:

What’s An Orthonormal Basis?

An Orthonormal basis is a set of vectors used to represent the state of a Quantum system in a complex vector space (Hilbert Space).

The word “Orthonormal” means the following:

For representing a quantum system in n-dimensions, the orthonormal basis will consist of a set of n unit kets that are orthogonal to each other.

In other words, the number of basis vectors equals the dimension of the vector space.

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