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# Questions tagged [qubo]

For questions about QUBO (quadratic unconstrained binary optimization).

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### Is it possible to transform MIQP into MILP without introducing new variable?

I have a QP optimization problem in the form $$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$ here $\bf Q$ is a symmetric matrix. $\bf x$ is the optimization variable, and it is binary. Is there a way to ...
• 2,377
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### vector number partitioning QUBO formulation

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 ...
• 101
3 votes
1 answer
160 views

### How to exponentiate binary variables in QUBO-type problems?

Ising Model In an Ising model, the Hamiltonian of one configuration of spins $\vec{s}$ is: $$H(\vec{s}, \mathcal{J}, \mathcal{h}) = \sum_{i} h_{i} s_{i} + \sum_{i \ne j}J_{ij} s_{i}s_{j}$$ where ...
• 523
7 votes
2 answers
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### Can QUBO solve this inverse Ising problem?

Inverse Ising Problem The inverse ising problem means fitting the coupling $J_{ij}$ and field $h_{i}$ parameters given a sample of configurations of spins. Each spin $s_{i}$ is either +1 or -1. The ...
• 523
4 votes
1 answer
256 views

### How do I arrive at the form given in this paper, for the QUBO version of the number partitioning problem?

In this article A new modeling and solution approach for the number partitioning problem1, it transforms the number partition problem into a QUBO form like equation (2.1) on page 2. \text{diff}=\...
4 votes
1 answer
359 views

### Why are the bounds 3 and 6 instead of 7, in this binary expansion of a slack variable in this QUBO problem?

I've recently started to study how to formulate optimization problems as QUBO models through this paper/tutorial: https://arxiv.org/pdf/1811.11538.pdf One of the steps is to transform the inequalities ...
15 votes
1 answer
1k views

### What is quadratization?

In the context of discrete optimization, what exactly does it mean to "quadratize" a function? The term seems to be used mainly by operations researchers, in my experience.
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