The Math behind
hi everyone, i'm not exactly a math champ, unfortunately, so it's very difficult for me to translate abstract mathematical formulas into practical examples / usage. once i manage to see the applied formula with figures (not just letters), it starts to make sense for me a little (e.g. VW ppt on traffic flow optimization, example for dummies).
i have a question for now, what is the difference between Hamiltionian formula, Ising formula, Qubo formula.
for me, all of the three look exactly (!) the same :-( just different letters.
sorry for my ignorance & cheers :-)
Comments
Hi Branislav -
The quick answer is that a QUBO expression assumes variables can only be 0 or 1. The Ising expression assumes variables can only be -1 or +1. The Hamiltonian expression is a formula to calculate the total energy in the system. For the D-Wave, you want the system to find solutions that minimize the total energy in the system.
In general, QUBO equations are more comfortable for people coming from a computer science background, whereas Ising equations are more comfortable for people coming from a physics background. However, regardless of one's background, sometimes a problem is easier to model with 0s and 1s, and sometimes a problem is easier to model with -1s and +1s.
Great answer, Thomas.
One thing to note is that it is very simple to convert between Ising and QUBO models. The linear terms (which multiply a single qubit) and quadratic terms (which multiply two qubits together) will have different values, but the structure is very similar. The only real difference is that in Ising, variables can be +1/-1 and in a QUBO, they can be 0/1.
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