Quantum Bayesian Networks

October 1, 2009

I, Grammaticus, speak about Quantum Computerization Versus Quantization

Filed under: Uncategorized — rrtucci @ 3:30 pm

Another installment in the “I Grammaticus” series. Previous posts in this series (1)here (on Quayle convention) and (2)here (on simulation).

I, Grammaticus, Caesar of the vast Roman Empire, have been warned by the god Jupiter, in a dream, to use the terms “quantization” and “quantum computerization” distinctly, or else there will be dire consequences for the future of Eternal Rome.

One quantizes a classical physical theory to get a corresponding quantum physical theory. One quantum computerizes a classical algorithm to obtain a quantum algorithm that produces the same answer as the classical one, but using some quantum means.

(Physical theories are in some sense algorithms, so maybe someday someone will show that there is a deep connection between quantization and q. computerization. Only Jupiter knows this.)

In the past, physicists have used the word “quantization” in the following fashion:

The classical picture of an atom, a bunch of negatively charged electrons in planetary orbits around a positively charged nucleus, leads to contradiction. Electrons are charged particles and charged particles radiate energy when they accelerate. In the planetary picture, the electrons would be accelerating (towards the nucleus), so they would radiate. This radiation would cause their orbits to decay, and they would soon plummet into their nucleus. So if the planetary picture of atoms were correct, all atoms would be unstable, which is certainly not what we observe. To fix this classical picture, we “quantize” classical mechanics. By this, we mean that we replace the deterministic classical theory by a probabilistic one. But not just any classical probabilistic one, but a quantum probabilistic theory, one where probabilities are built by taking the magnitude squared of a sum of complex “probability amplitudes”. In the quantum picture of an atom, the planetary orbits are replaced by a probability clould around the nucleus. The electrons are no longer accelerating so they do not radiate.

Besides quantizing the classical mechanics of point particles, physicists have also found it useful to quantize classical fields and strings. A classical field theory assigns a vector to each spacetime point. Quantizing classical field theories leads to Quantum Electrodynamics (QED) and ultimately to the Standard Model. A classical string theory assigns a classical string to each spacetime point. Quantizing classical string theories leads to String Theory.

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