Benchmarking Quantum Annealers with Near-Optimal Minor-Embedded Instances

Benchmarking Quantum Process Units (QPU) at an application level usually requires considering the whole programming stack of the quantum computer. One critical task is the minor-embedding (resp. transpilation) step, which involves space-time overheads for annealing-based (resp. gate-based) quantum computers. This paper establishes a new protocol to generate graph instances with their associated near-optimal minor-embedding mappings to D-Wave Quantum Annealers (QA). This set of favorable mappings is used to generate a wide diversity of optimization problem instances. We use this method to benchmark QA on large instances of unconstrained and constrained optimization problems and compare the performance of the QPU with efficient classical solvers. The benchmark aims to evaluate and quantify the key characteristics of instances that could benefit from the use of a quantum computer. In this context, existing QA seem best suited for unconstrained problems on instances with densities less than $10\%$. For constrained problems, the penalty terms used to encode the hard constraints restrict the performance of QA and suggest that these QPU will be less efficient on these problems of comparable size.