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On some features of Quadratic Unconstrained Binary Optimization with random coefficients

On some features of Quadratic Unconstrained Binary Optimization with random coefficients

Quadratic Unconstrained Binary Optimization (QUBO or UBQP) is concerned with maximizing/minimizing the quadratic form $H(J, \eta) = W \sum_{i,j} J_{i,j} \eta_{i} \eta_{j}$ with $J$ a matrix of coefficients, $\eta \in \{0, 1\}^N$ and $W$ a normalizing constant. In the statistical mechanics literature, QUBO is a lattice gas counterpart to the …