When we expand the Ising model we have one component with 3 qbits like Q1Q2Q3. But in qubo file we can only set coupling for 2 qbit only. How should I set this 3-qbit element to qubo file?


1 Answer 1


You need to introduce ancillary variables and minimize over them; which would enable you to have a QUBO form with only pairing terms. For example, if your binary variables are called $ x,y,z $ and you have a $ a*xyz $ term with the coefficient $ a$, you can use a technique of reduction by minimum selection where you introduce another variable $w$ such that this becomes a QUBO again:

$$\begin{align}\begin{aligned}axyz = aw ( x+y+z -2) \quad a<0\\axyz = a \left\{ w ( x+y+z -1) + (xy+yz+zx) - (x+y+z) +1 \right\} \quad a>0\end{aligned}\end{align} $$

This is explained in the D-Wave documentation.


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