Thursday, June 30, 2011

The Ising Model, Quantum Mechanics, and a Very Fast Computer

As I mentioned last week, we took a meeting with representatives from a quantum computing company based out of Canada. After all the explanations of quantum physics sailed right over my head, they said that their computer offers the ability to sample numbers from a Markov Random Field that has been simulated to steady state. In theory, this can also be done on a conventional computer, but it takes an impractical (damn near infinite) amount of time to reach steady state, before which the results don't mean much. The DWave gizmo can apparently do this in milliseconds.

So I started to cast around for some sort of explanation for what a Markov Random Field is, and I found this really neat book from 1980 which not only explains MRFs but also puts them in context of the Ising Model. The Ising Model is a statistical model that captures how the spins of ferromagnetic materials interact with each other and with an external field. The model then predicts the statistical likelihood of the overall distribution of those spins. A key element of this analysis is that system tries to reach a state of minimum energy, which means that as many spins as possible line up with each other and with the external field (if any).

Any stochastics problem that can be formulated into an expression of a MRF can be solved at great speed by the DWave quantum computer (or so it is claimed). My goal is to keep reading the book and then to develop a simple narrative and explanation (in Matlab, naturally) that captures the essence and power of this technique.

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