AI 中文总结
本研究通过比较驱动-耗散Kerr储层在不同相变下的表现，发现记忆增强源于内在Liouvillian弛豫谱中的有限速率模式，为设计耗散量子储层提供了物理基础。
AI 中文摘要
量子储层计算性能的提升已与动力学相变相关联，但这种联系是否延伸到耗散系统，以及哪些弛豫机制是其基础，仍未被充分理解。我们系统地比较了驱动-耗散Kerr储层在一阶和连续耗散相变中的表现，发现在两个相边界附近均增强了记忆和非线性处理能力。尽管在热力学极限下，Liouvillian能隙的闭合标志着相变，但计算性能通常并不遵循能隙抑制。一种精确的训练后Liouvillian模式分解将训练后的记忆定量归因于内在弛豫通道。该分解表明，能隙模式贡献较弱，而有限速率模式及其交叉贡献主导了增强的能力。这些结果超越了现象学相关性，直接将记忆能力与内在Liouvillian弛豫谱联系起来。此外，这些发现为设计耗散量子储层以及在实验可及的Kerr平台上测试记忆增强机制提供了物理基础。
英文摘要
Enhanced performance of quantum reservoir computing has been associated with dynamical phase transitions, but whether this connection extends to dissipative systems and which relaxation mechanisms underlie it remain insufficiently understood. We systematically compare driven-dissipative Kerr reservoirs across first-order and continuous dissipative phase transitions and find enhanced memory and nonlinear processing near both phase boundaries. Although the closure of the Liouvillian gap marks the transitions in the thermodynamic limit, computational performance does not generally follow gap suppression. An exact post-training Liouvillian-mode decomposition quantitatively attributes the trained memory to intrinsic relaxation channels. It shows that the gap mode contributes only weakly, while finite-rate modes and their cross-contributions dominate the enhanced capacity. These results go beyond phenomenological correlations by directly linking memory capacity to the intrinsic Liouvillian relaxation spectrum. Moreover, these findings provide a physical basis for designing dissipative quantum reservoirs and testing memory-enhancement mechanisms in experimentally accessible Kerr platforms.
Comments8 pages, 4 figures
