TY  - EJOUR
AU  - Schwägerl, Tim
AU  - Chai, Yahui
AU  - Hartung, Tobias
AU  - Jansen, Karl
AU  - Kühn, Stefan
TI  - Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice
IS  - arXiv:2408.03073
M1  - PUBDB-2024-05956
M1  - arXiv:2408.03073
PY  - 2024
AB  - Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed suitable for current noisy intermediate-scale quantum hardware. However, the resources required for training shallow variational quantum circuits often scale superpolynomially in problem size. In this study we numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark. For fixed resources, we compare the average performance of training a shallow variational quantum circuit, sampling with replacement, and a greedy algorithm starting from the same initial point as the quantum algorithm. We identify a minimum problem size for which the quantum algorithm can consistently outperform sampling and, for each problem size, characterize the separation between the quantum algorithm and the greedy algorithm. Furthermore, we extend the average case analysis by investigating the correlation between the performance of the algorithms by instance. Our results provide a step towards meaningful benchmarks of variational quantum algorithms for CO problems for a realistic set of resources.
LB  - PUB:(DE-HGF)25
DO  - DOI:10.3204/PUBDB-2024-05956
UR  - https://bib-pubdb1.desy.de/record/614736
ER  -