Albash, TameemMartín Mayor, VíctorHen, Itay2023-06-172023-06-172017-09-140031-900710.1103/PhysRevLett.119.110502https://hdl.handle.net/20.500.14352/18233© 2017 American Physical Society. T. A. and I. H. thank Daniel Lidar for useful comments on the manuscript. The computing resources were provided by the USC Center for High Performance Computing and Communications. T. A. was supported under ARO MURI Grant No. W911NF-11-1-0268, ARO MURI Grant No. W911NF-15-1-0582, and NSF Grant No. INSPIRE- 1551064. V. M.-M. was partially supported by MINECO (Spain) through Grant No. FIS2015-65078-C2-1-P (this contract partially funded by FEDER).Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.engjournal articlehttp://dx.doi.org/10.1103/PhysRevLett.119.110502https://journals.aps.orgrestricted access53Spin-glassModel.Física-Modelos matemáticos