Geng Liu

Xia Liu, Geng Liu, Jiaxin Huang et al.

Variational quantum algorithms (VQAs) are expected to establish valuable applications on near-term quantum computers. However, recent works have pointed out that the performance of VQAs greatly relies on the expressibility of the ansatzes and is seriously limited by optimization issues such as barren plateaus (i.e., vanishing gradients). This work proposes the state efficient ansatz (SEA) for accurate ground state preparation with improved trainability. We show that the SEA can generate an arbitrary pure state with much fewer parameters than a universal ansatz, making it efficient for tasks like ground state estimation. Then, we prove that barren plateaus can be efficiently mitigated by the SEA and the trainability can be further improved most quadratically by flexibly adjusting the entangling capability of the SEA. Finally, we investigate a plethora of examples in ground state estimation where we obtain significant improvements in the magnitude of cost gradient and the convergence speed.

Hao-Kai Zhang, Chengkai Zhu, Geng Liu et al.

Exploring quantum applications of near-term quantum devices is a rapidly growing field of quantum information science with both theoretical and practical interests. A leading paradigm to establish such near-term quantum applications is variational quantum algorithms (VQAs). These algorithms use a classical optimizer to train a parameterized quantum circuit to accomplish certain tasks, where the circuits are usually randomly initialized. In this work, we prove that for a broad class of such random circuits, the variation range of the cost function via adjusting any local quantum gate within the circuit vanishes exponentially in the number of qubits with a high probability. This result can unify the restrictions on gradient-based and gradient-free optimizations in a natural manner and reveal extra harsh constraints on the training landscapes of VQAs. Hence a fundamental limitation on the trainability of VQAs is unraveled, indicating the essential mechanism of the optimization hardness in the Hilbert space with exponential dimension. We further showcase the validity of our results with numerical simulations of representative VQAs. We believe that these results would deepen our understanding of the scalability of VQAs and shed light on the search for near-term quantum applications with advantages.

Geng Liu, Yuxi Wang

Domain generalization (DG) attempts to generalize a model trained on single or multiple source domains to the unseen target domain. Benefiting from the success of Visual-and-Language Pre-trained models in recent years, we argue that it is crucial for domain generalization by introducing extra text information. In this paper, we develop a novel Text-guided Domain Generalization (TDG) paradigm for domain generalization, which includes three following aspects. Specifically, we first devise an automatic words generation method to extend the description of current domains with novel domain-relevant words. Then, we embed the generated domain information into the text feature space, by the proposed prompt learning-based text feature generation method, which shares a common representation space with the image feature. Finally, we utilize both input image features and generated text features to train a specially designed classifier that generalizes well on unseen target domains, while the image encoder is also updated under the supervision of gradients back propagated from the classifier. Our experimental results show that the techniques incorporated by TDG contribute to the performance in an easy implementation manner. Experimental results on several domain generalization benchmarks show that our proposed framework achieves superior performance by effectively leveraging generated text information in domain generalization.