用于量子动力学预测的互补矩阵门控QKAN快速权重编程器
Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting
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中文总结 AI 辅助
该研究针对量子动力学预测的快速权重编程器，提出互补矩阵门控的自调制QKAN快速权重编程器，在多步量子动力学预测中较标量门控模型提升91.2%以上，均方误差达0.001量级。
中文摘要 AI 辅助
序列模型必须决定将信息写入内存还是保留。在量子及类量子序列学习中，非线性循环更新常需重复的电路评估与随时间的序列反向传播，导致长上下文处理成本高昂。基于类量子柯尔莫哥洛夫-阿诺德网络（QKAN）的门控快速权重编程器（FWPs）通过将上下文存储于时变快速参数缓解了这一瓶颈，但其标量门对每个快速状态坐标采用统一的保留-写入平衡，迫使所有参数共享同一内存时间尺度。我们提出自调制QKAN基FWPs，将该广播门替换为对新提议分支、有界旧状态分支或两者的低秩生成元素级调制；进一步提出互补矩阵门控（CMG），其使用一个sigmoid矩阵门保留旧状态，其补门用于写入新提议，在保留标量门的有界凸更新与仿射前缀扫描结构的同时，提供坐标级内存控制，调制头成本为单分支规则。我们在结合经典与QKAN基慢、快速编程器的四种FWP架构上，对比了四种自调制规则与标量门；在七个单步预测基准及五个序列长度上，CMG对快速编程器含QKAN基模块的架构提供最一致的改进。在使用CUDA-Q Dynamics模拟的Jaynes-Cummings与transmon谐振器动力学的直接多步预测中，CMG模型在4、8、16步预测范围内均保持0.001量级或更低的均方误差，较标量门控对应模型至少提升91.2%。这些结果表明，坐标级互补调制是QKAN基FWPs的稳定有效更新方式。
英文摘要
Sequence models must decide what to write into memory and what to retain. In quantum and quantum-inspired sequence learning, nonlinear recurrent updates often require repeated circuit evaluations and sequential backpropagation through time, making long contexts costly. Gated fast-weight programmers (FWPs) based on quantum-inspired Kolmogorov-Arnold networks (QKANs) alleviate this bottleneck by storing context in time-varying fast parameters. However, their scalar gate applies one retention-write balance to every fast-state coordinate, forcing all parameters to share a memory timescale. We introduce Self-Modulating QKAN-based FWPs, which replace this broadcast gate with low-rank-generated element-wise modulation of the new-proposal branch, a bounded old-state branch, or both. We further propose Complementary Matrix Gating (CMG), which uses one sigmoid matrix gate to retain the old state and its complement to write the new proposal. CMG provides coordinate-wise memory control while preserving the bounded convex update and affine prefix-scan structure of scalar gating, at the modulation-head cost of a single-branch rule. We compare four self-modulating rules with scalar gating across four FWP architectures combining classical and QKAN-based slow and fast programmers. Across seven single-step forecasting benchmarks and five sequence lengths, CMG gives the most consistent improvements for architectures whose fast programmer incorporates a QKAN-based module. In direct multi-step forecasting of Jaynes-Cummings and transmon-resonator dynamics simulated with CUDA-Q Dynamics, CMG models maintain mean-squared errors on the order of 0.001 or lower across forecasting horizons of 4, 8, and 16 steps, while improving on their scalar-gated counterparts by at least 91.2%. These results establish coordinate-wise complementary modulation as a stable and effective update for QKAN-based FWPs.
发表机构
- National Taiwan University（国立台湾大学）
- National Center for High-Performance Computing, National Institutes of Applied Research（国家高性能计算中心（国家应用研究院））
- NVIDIA AI Technology Center, NVIDIA Corp.（英伟达AI技术中心，英伟达公司）
- Center for Quantum Science and Engineering, National Taiwan University（国立台湾大学量子科学与工程研究中心）
- Graduate Institute of Applied Physics, National Taiwan University（国立台湾大学应用物理学研究所）
- National Yang Ming Chiao Tung University（国立阳明交通大学）
- Halmstad University（哈尔姆斯塔德大学）
- Korea Advanced Institute of Science and Technology（韩国科学技术院）
- Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（哈马德·本·哈利法大学卡塔尔量子计算中心，科学与工程学院）
- National Center for Theoretical Sciences（国家理论科学中心）
机构由 AI 辅助整理，请以论文原文为准。
