Zijun Chen

Daocheng Fu, Jianlong Chen, Renqiu Xia et al.

Mathematical geometric problem solving (GPS) demands verifiable logical coherence and multimodal reasoning capabilities. While large language models (LLMs) have shown rapid progress in GPS, their advancement is hindered by the lack of reliable benchmarks and systematic methodologies. A critical challenge is the inherent hallucination in LLMs, which leads to synthetic GPS datasets that are often noisy, unverified, and self-contradictory. To address this, we introduce TrustGeoGen, a data engine that generates formally verified geometric problems to establish a principled and trustworthy benchmark. Our engine integrates four key innovations: 1) Multimodal Alignment, which synchronizes the generation of diagrams, text, and step-by-step solutions; 2) Formal Verification, ensuring all reasoning paths are rule-compliant; 3) Connection Thinking, bridging formal deduction with human-like logical steps; and 4) our \textit{GeoExplore} series algorithms, which produce diverse problem variants with multiple solutions and self-reflective backtracking. Using this engine, we create the GeoTrust-200K dataset and the corresponding GeoTrust-test benchmark, both with guaranteed cross-modal integrity. Experiments reveal that state-of-the-art models achieve only 45.83\% accuracy on GeoTrust-test, highlighting its significant challenge. Furthermore, training on our synthesized data substantially improves model performance on GPS tasks, with strong generalization to out-of-domain (OOD) benchmarks. Our code and data are available at https://github.com/Alpha-Innovator/TrustGeoGen

Murphy Yuezhen Niu, Vadim Smelyanskyi, Paul Klimov et al.

Two-level-system (TLS) defects in amorphous dielectrics are a major source of noise and decoherence in solid-state qubits. Gate-dependent non-Markovian errors caused by TLS-qubit coupling are detrimental to fault-tolerant quantum computation and have not been rigorously treated in the existing literature. In this work, we derive the non-Markovian dynamics between TLS and qubits during a SWAP-like two-qubit gate and the associated average gate fidelity for frequency-tunable Transmon qubits. This gate dependent error model facilitates using qubits as sensors to simultaneously learn practical imperfections in both the qubit's environment and control waveforms. We combine the-state-of-art machine learning algorithm with Moiré-enhanced swap spectroscopy to achieve robust learning using noisy experimental data. Deep neural networks are used to represent the functional map from experimental data to TLS parameters and are trained through an evolutionary algorithm. Our method achieves the highest learning efficiency and robustness against experimental imperfections to-date, representing an important step towards in-situ quantum control optimization over environmental and control defects.