On the Influence of Numerical Representations in Quantum-Annealing-Based Linear Regression

Quantum annealers are a class of quantum technologies that have attracted increasing attention due to their natural suitability for solving combinatorial optimization problems. Recent works reformulated the linear regression as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling its implementation on quantum annealers and offering potential speed-ups for large datasets. However, this QUBO-based formulation requires the definition of a precision vector to represent the real-valued regression coefficients as integers variables, which introduces limitations related to the quantization accuracy. In this work, we investigate several numerical representations strategies for defining the precision vector. By performing a set of numerical experiments, we analyze the performance of these strategies in different configurations. Our results that the strategy usually known as conventional binary representation provides the best trade-off between performance and resource efficiency for quantum-assisted linear regression.