Liming Zhao

Liming Zhao, Naixu Guo, Ming-Xing Luo et al. · berkeley

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature Gibbs states. Other works consider a weaker sense of learning, such as PAC learning and shadow tomography. In this work, we consider learning states that are close to neural network quantum states, which can efficiently be represented by a graphical model called restricted Boltzmann machines (RBMs). To this end, we exhibit robustness results for efficient provable two-hop neighborhood learning algorithms for ferromagnetic and locally consistent RBMs. We consider the $L_p$-norm as a measure of closeness, including both total variation distance and max-norm distance in the limit. Our results allow certain quantum states to be learned with a sample complexity \textit{exponentially} better than naive tomography. We hence provide new classes of efficiently learnable quantum states and apply new strategies to learn them.

Liming Zhao, Aman Agrawal, Patrick Rebentrost

Restricted Boltzmann Machines (RBMs) are widely used probabilistic undirected graphical models with visible and latent nodes, playing an important role in statistics and machine learning. The task of structure learning for RBMs involves inferring the underlying graph by using samples from the visible nodes. Specifically, learning the two-hop neighbors of each visible node allows for the inference of the graph structure. Prior research has addressed the structure learning problem for specific classes of RBMs, namely ferromagnetic and locally consistent RBMs. In this paper, we extend the scope to the quantum computing domain and propose corresponding quantum algorithms for this problem. Our study demonstrates that the proposed quantum algorithms yield a polynomial speedup compared to the classical algorithms for learning the structure of these two classes of RBMs.

Lele Cheng, Xiangzeng Zhou, Liming Zhao et al.

In many real-world datasets, like WebVision, the performance of DNN based classifier is often limited by the noisy labeled data. To tackle this problem, some image related side information, such as captions and tags, often reveal underlying relationships across images. In this paper, we present an efficient weakly supervised learning by using a Side Information Network (SINet), which aims to effectively carry out a large scale classification with severely noisy labels. The proposed SINet consists of a visual prototype module and a noise weighting module. The visual prototype module is designed to generate a compact representation for each category by introducing the side information. The noise weighting module aims to estimate the correctness of each noisy image and produce a confidence score for image ranking during the training procedure. The propsed SINet can largely alleviate the negative impact of noisy image labels, and is beneficial to train a high performance CNN based classifier. Besides, we released a fine-grained product dataset called AliProducts, which contains more than 2.5 million noisy web images crawled from the internet by using queries generated from 50,000 fine-grained semantic classes. Extensive experiments on several popular benchmarks (i.e. Webvision, ImageNet and Clothing-1M) and our proposed AliProducts achieve state-of-the-art performance. The SINet has won the first place in the classification task on WebVision Challenge 2019, and outperformed other competitors by a large margin.

Yunpu Ma, Volker Tresp, Liming Zhao et al.

In this work, we propose the first quantum Ansätze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.