Variational Amplitude Amplification for Solving QUBO Problems

• URL: http://arxiv.org/abs/2301.13665v2
• Date: Wed, 1 Feb 2023 15:36:31 GMT
• Title: Variational Amplitude Amplification for Solving QUBO Problems
• Authors: Daniel Koch, Massimiliano Cutugno, Saahil Patel, Laura Wessing, Paul M. Alsing
• Abstract summary: This study focuses on QUBO (quadratic unconstrained binary optimization) problems, which are well-suited for qubit superposition states. We demonstrate circuit designs which encode QUBOs as cost oracle' operations $U_textrmC$, which when combined with the standard Grover diffusion operator $U_textrms$ lead to high probabilities of measurement for states corresponding to the optimal and near optimal solutions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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