Variational autoencoders (VAEs) are powerful generative models with the
salient ability to perform inference. Here, we introduce a quantum variational
autoencoder (QVAE): a VAE whose latent generative process is implemented as a
quantum Boltzmann machine (QBM). We show that our model can be trained
end-to-end by maximizing a well-defined loss-function: a 'quantum' lower-bound
to a variational approximation of the log-likelihood. We use quantum Monte
Carlo (QMC) simulations to train and evaluate the performance of QVAEs. To
achieve the best performance, we first create a VAE platform with discrete
latent space generated by a restricted Boltzmann machine (RBM). Our model
achieves state-of-the-art performance on the MNIST dataset when compared
against similar approaches that only involve discrete variables in the
generative process. We consider QVAEs with a smaller number of latent units to
be able to perform QMC simulations, which are computationally expensive. We
show that QVAEs can be trained effectively in regimes where quantum effects are
relevant despite training via the quantum bound. Our findings open the way to
the use of quantum computers to train QVAEs to achieve competitive performance
for generative models. Placing a QBM in the latent space of a VAE leverages the
full potential of current and next-generation quantum computers as sampling
devices.

使用量子玻尔兹曼机实现的量子变分自编码器（QVAE）比仅涉及生成过程中的离散变量的相似方法在 MNIST 数据集上实现了最先进的性能。将 QBM 放置在 VAE 的潜在空间中将充分发挥当前和下一代量子计算机作为采样设备的潜力。

量子变分自编码器

Quantum Variational Autoencoder

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 transverse-field Ising Hamiltonian. Due to the
non-commutative 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 like D-Wave for QBM training and application.

本文提出了一种新的基于量子玻尔兹曼分布的机器学习方法，即量子玻尔兹曼机。通过对量子概率引入边界，可以使该机器学习模型的训练高效进行，同时也探讨了使用 D-Wave 等量子退火处理器进行训练和应用的可能性。