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arXiv · 2301.13665

Variational Amplitude Amplification for Solving QUBO Problems

Daniel Koch·Massimiliano Cutugno·Saahil Patel·Laura Wessing·Paul M. Alsing
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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.

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Daniel Koch, Massimiliano Cutugno, Saahil Patel, Laura Wessing, Paul M. Alsing. 2023-01-31. Variational Amplitude Amplification for Solving QUBO Problems. https://arxiv.org/abs/2301.13665

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