A guide on Grover search algorithms for solving QUBO problems

Kurzfassung

Typical industry-related optimizations, like routing, packing, or scheduling, can be reformulated as a quadratic unconstrained binary optimization (QUBO) problem [1]. In the fault-tolerant quantum computing era, a promising approach to solve these problems is the Grover Adaptive Search [2]. The Grover Adaptive Search is able to solve QUBOs with a quadratic speed-up in comparison to classical algorithms. Here different Grover runs are chained together in order to identify the optimal solution.

In this poster, we present a comprehensive guide with intuitive visuals, a theoretical background and a walkthrough to help non-expert to apply the Grover Adaptive Search. In particular, we demonstrate how to parse the QUBOs into a Grover oracle - the quantum dictionary [3] - and what this implies for the different quantum registers involved.

[1] G. Kochenberger, J.-K. Hao, F. Glover, M. Lewis, Z. Lü, H. Wang, and Y. Wang, J. Comb. Optim. 28, 58 (2014).

[2] W. P. Baritompa, D. W. Bulger, and G. R. Wood, SIAM J. Optim. 15, 1170 (2005).

[3] A. Gilliam, C. Venci, S. Muralidharan, V. Dorum, E. May, R. Narasimhan, and C. Gonciulea, arXiv:1907.11513 (2019).