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I would like to implement an adaptation of the number partitioning QUBO formulation. The original one is described in this paper as well as this thread on this forum

The version of my problem is the following: instead of having a set of 1D numbers, I have a set of $ m $-dimensions vectors, e.g: $ \vec{w} = (\vec{w_1}, \vec{w_2},..., \vec{w_n})$ where $ \vec{w_i} = (w_{i1}, ..., w_{im}) $, and I want to partition this set $ \vec{w} $ such that the difference of $ (w_{1j}x_1, w_{2j}x_2,..., w_{nj}x_n) $ is minimized for each $ j \in m $

What would be the QUBO formulation for this version of the number partitioning ?

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