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.

中文翻译：

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量子退火优化器的温度缩放定律

量子退火的物理实现不可避免地在有限的温度下运行。我们指出了固定有限温度量子退火器的一个基本局限性，即它不能充当竞争性的可扩展优化器，并表明要用作优化器，退火器温度必须根据问题的大小适当缩小。我们推导了一个温度标度定律，该定律规定温度必须至少以对数方式下降，但也可能是具有问题大小的幂定律。我们通过实验和模拟证实了我们的结果，并讨论了这些对实际退火炉的影响。