Kefan Cao | Searcharxiv

arXiv2026

Irreversibility Enhances Quantum-Enhanced Markov-Chain Monte Carlo

Detailed balance underlies conventional Markov-chain Monte Carlo (MCMC) algorithms. Yet in classical systems, breaking detailed balance generates irreversible probability currents and can accelerate sampling. Whether irreversibility can similarly enhance quantum MCMC remains an intriguing question. Here we show that irreversibility provides a new route to improving the recent quantum-enhanced MCMC (QEMC), which combines quantum proposals with classical acceptance. By introducing state-dependent proposals that break detailed balance while preserving the target stationary distribution, we develop an irreversible quantum-enhanced Monte Carlo (IQEMC). Guided by Landau-Zener transitions, IQEMC promotes large energy descents from high-energy states while maintaining stable transitions near low-energy states. On spin-glass benchmarks, IQEMC outperforms QEMC without increasing computational complexity and, unlike the annealing baseline, exhibits a spectral gap that increases with system size and annealing speed. These results establish irreversibility as a physically grounded mechanism for enhancing quantum MCMC.

cond-mat.stat-mech↗

arXiv2025

Orthogonal Low-rank Adaptation in Lie Groups for Continual Learning of Large Language Models

Large language models (LLMs) suffer from catastrophic forgetting in sequential multi-task learning. Existing parameter regularization methods (e.g., O-LoRA, N-LoRA) mitigate interference via low-rank subspace orthogonality, but additive updates distort the intrinsic geometry of model parameters. We propose \textbf{OLieRA}, a Lie group based fine-tuning framework that preserves parameter geometry through multiplicative updates while enforcing orthogonality across task subspaces. OLieRA achieves state-of-the-art performance on the Standard CL benchmark and remains highly competitive under large task sequences. It further inherits the replay-free and task-ID free inference properties of O-LoRA, establishing a principled paradigm for continual learning in LLMs.

cs.CL↗