Quantum Boltzmann Machine

Inspired by the success of Boltzmann machines based on classical Boltzmann distribution, we propose a new machine-learning approach based on quantum Boltzmann distribution of a quantum Hamiltonian. Because of the noncommutative nature of quantum mechanics, the training process of the quantum Boltzmann machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors for QBM training and application.

受基于经典玻尔兹曼分布的玻尔兹曼机成功的启发，我们提出了一种基于量子哈密顿量的量子玻尔兹曼分布的新机器学习方法。由于量子力学的非对易性质，量子玻尔兹曼机（QBM）的训练过程可能变得不平凡。我们通过引入量子概率的界限来规避这个问题。这使我们能够通过采样有效地训练QBM。我们展示了有界和无界情况下使用精确对角化进行QBM训练的示例，并将结果与经典玻尔兹曼训练进行了比较。我们还讨论了使用量子退火处理器进行QBM训练和应用的可能性。