Variational Amplitude Amplification for Solving QUBO Problems

Abstract

We investigate the use of amplitude amplification on the gate-based model of quantum computing
 as a means for solving combinatorial optimization problems. This study focuses primarily on
 QUBO (quadratic unconstrained binary optimization) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as ‘cost oracle’
 operations UC, which when combined with the standard Grover diffusion operator Us lead to high
 probabilities of measurement for states corresponding to the optimal and near optimal solutions. In
 order to achieve these probabilities, a single scalar parameter ps is required, which we show can be
 found through a variational quantum-classical hybrid approach.