Variational Amplitude Amplification for Solving QUBO Problems

TL;DR

This paper presents a variational quantum algorithm that uses amplitude amplification to efficiently solve QUBO problems on gate-based quantum computers, combining circuit design with a hybrid parameter optimization.

Contribution

It introduces a novel circuit design for encoding QUBO problems as cost oracles and a variational method to optimize amplification parameters.

Findings

Circuit designs encode QUBOs as cost oracles for amplitude amplification.

A variational approach finds optimal amplification parameters.

Enhanced probability of measuring optimal solutions.

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 $U_{\textrm{C}}$, which when combined with the standard Grover diffusion operator $U_{\textrm{s}}$ 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 $p_{\textrm{s}}$ is required, which we show can be found through a variational quantum-classical hybrid approach.