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An Introduction To The Hilbert Space
The space where quantum systems live and breathe.
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.
If you’ve been a student of Classical Physics, you must have plotted the state of a particle in a 3D Cartesian space.
But unlike a classical particle here, a quantum system is represented using a Hilbert Space.
A Hilbert Space is a vector space with either a finite or infinite number of dimensions.
Its elements are Kets, which represent quantum systems.
(If you’re unfamiliar with Ket and Bra vectors, starting with the lesson titled “An Introduction To Bra-Ket (Dirac) Notation” is highly recommended.)
Visualizing The Hilbert Space
A single qubit can be represented using a 2-dimensional Hilbert space.
Just like i and j, which are basis vectors for a classical 2D space, the basis vectors for a 2D Hibert space representing a qubit are ∣0⟩ and ∣1⟩.
Similar to i and j, these are orthonormal to each other.
- Ortho: Perpendicular to each…
