Ciro Santilli @cirosantilli 37

Good modern OpenGL tutorial in retained mode with shaders, see also: stackoverflow.com/questions/6733934/what-does-immediate-mode-mean-in-opengl/36166310#36166310

where:

Note that this is the sum of the:Note that the relationship between $\psi$ and $F$ is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore $F$

As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):

In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.

The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.

Technique that uses multiple non-ideal qubits (physical qubits) to simulate/produce one perfect qubit (logical).

One is philosophically reminded of classical error correction codes, where we also have multiple input bits per actual information bit.

TODO understand in detail. This appears to be a fundamental technique since all physical systems we can manufacture are imperfect.

Part of the fundamental interest of this technique is due to the quantum threshold theorem.

For example, when PsiQuantum raised 215M in 2020, they announced that they intended to reach 1 million physical qubits, which would achieve between 100 and 300 logical qubits.

Video "Jeremy O'Brien: "Quantum Technologies" by GoogleTechTalks (2014)" youtu.be/7wCBkAQYBZA?t=2778 describes an error correction approach for a photonic quantum computer.

Bibliography:

Directly modelled by group.

For continuous symmetries, see: Lie group.

Originally by Springer, but later moved to the European mathematical society.

TODO: I'm surprised that the Wiki page barely talks about it, and there are few Google hits too! A sample one: www.researchgate.net/publication/228928756_On_the_existence_and_uniqueness_of_Maxwell's_equations_in_bounded_domains_with_application_to_magnetotellurics

An "alternative" formulation of quantum mechanics that does not involve operators.

Same value if you swap any input arguments.