Unlink most basic explanations of this topic I’ll start with a technical statement:
<aside> 💡 The idea is to encode a problem’s variables as spins in an Ising model, to cause these spins to interact with each other so that the total energy is minimized when the spins encode the values which are the solution of the problem, and then to exploit the Adiabatic Theorem to find this state.
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In order to understand this we need to understand what I mean by these things:
Once you see this, I’ll show you an example which will make it clear what it means to encode something with spins.
An Ising Model is a lattice like this:
Each little circle is a so-called spin, which is what physicists call pretty much any system which has just two states. The name comes from particles which have intrinsic angular momentum (spin) always appears as either clockwise or counterclockwise along whatever axis you measure it, so it’s an example of a two-state system:
The red and green lines between it are supposed to signify that pairs of spins can like to be the same or opposite each other. The thicker the line the stronger the preference.
aside: It’s easy to get overwhelmed with the physics background when learning something like this. All my life I’ve been getting suck on background instead of accepting things as postulates and learning what’s in front of me. I promise that this really is one of those topic where that works! You don’t need to worry about the underlying quantum mechanics to get a sense of what’s going on.
When two spins are the same but they want to be opposite (when they have a red line between them) there is energy in that interaction. You already intuitively understand this if you’ve ever tried to hold two magnets against each other the wrong way with both Norths pointing the same way. It looks innocuous enough but the minute you let go the potential energy stored up in that interaction (in the magnetic field) causes them to jump apart.
Let’s say the spins can be either 1 = up or -1 = down and give them names s_1 and s_2. So the energy is given by
$$ E = s_1 I\, s_2 $$
Where I is the interaction between the two spins.