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.

翻译：在应用层面对量子处理单元进行基准测试通常需要考虑量子计算机的完整编程栈。一个关键步骤是小嵌入（对应门基量子计算机的转译）环节，该环节会为退火基（对应门基）量子计算机引入时空开销。本文提出一种新协议，用于生成图实例及其对应的D-Wave量子退火器近优小嵌入映射。这组优化映射被用于生成多样化的优化问题实例。我们采用该方法对无约束和约束优化问题的大规模实例进行量子退火器基准测试，并将量子处理单元的性能与高效经典求解器进行比较。该基准测试旨在评估和量化能够从量子计算机使用中受益的实例关键特征。在此背景下，现有量子退火器似乎最适合处理密度低于$10\%$的实例上的无约束问题。对于约束问题，用于编码硬约束的惩罚项限制了量子退火器的性能，表明这些量子处理单元在可比规模问题上效率较低。