Inequalities cannot be directly converted into a qubo form

0⩽ Expression ⩽ N

We can introduce a slack variable and convert it to an equality problem:

⟹ Expression + s = N where: s ∈ Z, s ∈ [0,N]

Since the slack variables, being encoded on a quantum computer, can hold only discrete values(0, 1, 2...N) the expression also must be of a discrete nature and be of the same values(0, 1, 2...N) to satisfy the constraint.

How to encode inequality constraints when the expression is discrete but the values of the expression have sporadic(and maybe unknown) intervals(0, 1.2, 1.5, 3.8....N).


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