Benchmarking Quantum Annealers with Linear System Solving

While we are still far from Fault Tolerant Quantum Computers (FTQCs) which are required to obtain a significant advantage in some algorithms, for benchmarking purposes, it can be interesting to try and solve problems with Noisy Intermediate Scale Quantum (NISQ) era Quantum Computers (QCs) on some of the future applications of FTQC. In this paper, our aim is to assess the performance of D-Wave Quantum Processing Units (QPUs) in solving systems of linear equations. This can also be used as a first reference point to compare NISQ era QPUs between them. To that end, we illustrate the transformation of these systems into Quadratic Unconstrained Binary Optimization (QUBO) problems, which can be tackled by these QPUs. We evaluate their performance in their default configurations and demonstrate some usual way to enhance their performance. Finally, we introduce a novel approach to solving these problems that does not result in an exponential growth of their coefficients. Data-points from these experiments are meant to be integrated in the BACQ benchmark [2].