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An increase in the efficiency of sampling from Boltzmann distributions wouldhave a significant impact on deep learning and other machine-learningapplications. Recently, quantum annealers have been proposed as a potentialcandidate to speed up this task, but several limitations still bar thesestate-of-the-art technologies from being used effectively. One of the mainlimitations is that, while the device may indeed sample from a Boltzmann-likedistribution, quantum dynamical arguments suggest it will do so with an {\itinstance-dependent} effective temperature, different from its physicaltemperature. Unless this unknown temperature can be unveiled, it might not bepossible to effectively use a quantum annealer for Boltzmann sampling. In thiswork, we propose a strategy to overcome this challenge with a simpleeffective-temperature estimation algorithm. We provide a systematic studyassessing the impact of the effective temperatures in the learning of a specialclass of a restricted Boltzmann machine embedded on quantum hardware, which canserve as a building block for deep-learning architectures. We also provide acomparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100.Although assuming a suitable fixed effective temperature also allows us tooutperform one step contrastive divergence (CD-1), only when using aninstance-dependent effective temperature do we find a performance close to thatof CD-100 for the case studied here.

Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning