Yilun Yang

Zhiyan Ding, Lin Lin, Yilun Yang et al.

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is $\#\textsf{BQP}$-complete in the worst case. In this work, we introduce QFAMES (Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

Yilun Yang, Yekun Chai

Code-mixing, the practice of switching between languages within a conversation, poses unique challenges for traditional NLP. Existing benchmarks are limited by their narrow language pairs and tasks, failing to adequately assess large language models' (LLMs) code-mixing abilities. Despite the recognized importance of code-mixing for multilingual users, research on LLMs in this context remains sparse. Additionally, current techniques for synthesizing code-mixed data are underdeveloped to generate code-mixing. In response, we introduce CodeMixBench, a comprehensive benchmark covering eight tasks, including three specific to LLMs and five traditional NLP tasks, and 18 languages across seven language families. We also propose a new method for generating large-scale synthetic code-mixed texts by combining word substitution with GPT-4 prompting. Our evaluation reveals consistent underperformance of LLMs on code-mixed datasets involving different language families. Enhancements in training data size, model scale, and few-shot learning could improve their performance. The code and dataset are available at https://github.com/Jeromeyluck/CodeMixBench.

Fan Fei, Zhan Tu, Yilun Yang et al.

Insects and hummingbirds exhibit extraordinary flight capabilities and can simultaneously master seemingly conflicting goals: stable hovering and aggressive maneuvering, unmatched by small scale man-made vehicles. Flapping Wing Micro Air Vehicles (FWMAVs) hold great promise for closing this performance gap. However, design and control of such systems remain challenging due to various constraints. Here, we present an open source high fidelity dynamic simulation for FWMAVs to serve as a testbed for the design, optimization and flight control of FWMAVs. For simulation validation, we recreated the hummingbird-scale robot developed in our lab in the simulation. System identification was performed to obtain the model parameters. The force generation, open-loop and closed-loop dynamic response between simulated and experimental flights were compared and validated. The unsteady aerodynamics and the highly nonlinear flight dynamics present challenging control problems for conventional and learning control algorithms such as Reinforcement Learning. The interface of the simulation is fully compatible with OpenAI Gym environment. As a benchmark study, we present a linear controller for hovering stabilization and a Deep Reinforcement Learning control policy for goal-directed maneuvering. Finally, we demonstrate direct simulation-to-real transfer of both control policies onto the physical robot, further demonstrating the fidelity of the simulation.