The paper explores the impact of logical qubit encoding on the minimum spectral gap of the problem Hamiltonian in quantum annealing. It shows that denser encodings, such as cliques, require lower chain strengths to maintain ferromagnetic couplings compared to sparser encodings like chains. This is desirable as coupler strength rescaling, a common issue on quantum hardware, reduces the minimum spectral gap.
The analysis of chain breaks for different embeddings of the same instance reveals that the optimal chain strength varies depending on the embedding method used. This observation leads to the design of a simple heuristic that efficiently finds the optimal chain strength for each instance. The heuristic uses the chain break rate as the optimization criterion and converges in just a few preprocessing steps, significantly reducing the time required compared to a full chain strength scan. Experiments show that this heuristic can improve the quality of the best solution by up to 17.2% compared to the default method on D-Wave systems.
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