Generating Presence-Absence Matrices by Quantum Annealing

We consider the problem of generating binary matrices with fixed sums for their rows and columns coefficients, i.e. with fixed margins. Such presence-absence (0/1) matrices are widely used in ecological research, for instance to represent the presence or absence of particular species in a particular habitat. Generating random matrices with fixed sums for their rows and their columns is an important issue in order to compare some given matrix presenting field data versus randomly generated matrices with similar characteristics (same sums on rows and columns) in order to test some hypothesis, i.e. when performing null model statistical analysis. We propose to model this problem in QUBO (Quadratic Unconstrained Binary Optimization) in order to solve it by quantum annealing. QUBO is the input language of quantum computers based on quantum annealing such as the D-Wave systems and of “quantum-inspired” annealing solvers based on dedicated classical hardware. We present some experimental results achieved on the D-Wave Advantage quantum computer and on the Fixstars Amplify Annealing Engine.