Comment on “ Scaling advantages of all-to-all connectivity in physical annealers : the Coherent Ising Machine vs D-Wave 2000 Q ”

We demonstrate an exponential O(e 2))) penalty in performance for the D-Wave quantum annealer relative to coherent Ising machines when solving Ising problems on dense graphs, which is attributable to the differences in internal connectivity between the machines. This leads to a severalorders-of-magnitude time-to-solution difference between coherent Ising machines and the D-Wave system for problems with over 50 vertices. Our results provide strong experimental support to efforts to increase the connectivity of physical annealers. The starting premise, that physical connectivity plays a role in performance of these systems, has been well discussed in the literature and is not in dispute. The conclusion, in support of increased connectivity in physical annealers, aligns with ongoing work at D-Wave and elsewhere to build next-generation quantum systems with ∗ cmcgeoch@dwavesys.com denser connection topologies. However, the remaining claims in this excerpt are based on flawed analysis and faulty reasoning about what conclusions can legitimately be drawn from the data: 1. The “exponential O(e 2)))” performance gap is based on two regression models that are meant to describe scaling of the algorithms realized by the 2000Q processor and the CIM. However, the authors have fit their models incorrectly, to data that does not correspond to the true scaling of these algorithms. The resulting curves overestimate scaling of the 2000Q processor and underestimate scaling of the CIM. 2. The “several-orders-of-magnitude” difference in TTS is based on extrapolating those incorrect curves to large problems well outside the range of tests. Looking at the measured data, the CIM appears to be about 100x and 8000x faster on SK and dense MC inputs, respectively. However, an applesto-apples analysis of their data (treating post processing the same way for both systems) shows much smaller gaps: the CIM is about 5x faster on SK and 364x faster on dense MC inputs. That gap might have been further reduced, or perhaps eliminated, if the tests had incorporated performance-tuning features available on the 2000Q processor. The following sections discuss these issues in more detail. First, however, we remark that even if the CIM is faster on dense SK and MC inputs (and the 2000Q system is faster on sparse inputs, as described in [1,3]), there is nothing in the paper to suggest that this result is representative of performance on inputs that matter. That is, many classical optimization algorithms, such as simulated annealing and the CIM, work by stepping through a large space of possible solutions one at a time. Some inputs are combinatorially easy, requiring just a few steps and time scales in fractions of seconds to be solved; some inputs are combinatorially hard, requiring an enormous number of steps and time scales in hours, weeks, or years, to be solved. D-Wave quantum processors work under a completely different paradigm: instead of of stepping through the