用于在量子计算机上模拟聚合动力学的速率矩阵的显式块编码
Explicit block encodings of rate matrices for simulating polymerization kinetics on quantum computers
浏览论文内容
中文总结 AI 辅助
本文提出在量子计算机上通过显式块编码速率矩阵模拟聚合动力学，采用稀疏预言机和LCU分解方法，实现指数级内存节省，为容错量子硬件上的聚合物模拟奠定基础。
中文摘要 AI 辅助
预测聚合过程中分子量分布和单体序列如何演化是聚合物科学的核心问题，然而经典方法面临着分子分辨率与计算成本之间的权衡：对于共聚物，可区分物种的数量随链长呈指数增长。量子计算提供了一种潜在的替代方案，前提是控制动力学的非酉速率矩阵能够嵌入到酉量子电路中，这一任务被称为块编码。在此，我们为活性聚合的两种动力学模型构建了显式块编码电路：模型A，单单体聚合，其下双对角速率矩阵通过稀疏预言机构造和两项酉算子线性组合（LCU）分解进行编码；模型B，双单体共聚，其中通过整数索引（m-索引）对聚合物物种进行双射标记，产生结构化的稀疏矩阵，可通过五项LCU或稀疏预言机构造进行编码。使用稀疏预言机编码的数值模拟重现了经典时间演化，其反应比取自已报道的烯烃共聚体系，涵盖近无规（$r_1 r_2 \simeq 1$）和嵌段（$r_1 r_2 > 1$）微结构，并通过显式重构编码矩阵块验证了LCU编码。资源估算表明，两种实现仅需$O(\log N)$个量子比特（相对于矩阵维度$N$，相比经典状态空间实现指数级内存节省），门数逐渐增长，在$10^3$个系统量子比特时达到$10^4$至$10^5$个门。这些结果为在容错量子硬件上模拟聚合动力学奠定了具体的量子电路基础，并朝着利用指数级状态空间压缩处理高维聚合物反应网络迈出了第一步。
英文摘要
Predicting how molecular weight distribution and monomer sequence evolve during polymerization is central to polymer science, yet classical approaches face a trade-off between molecular resolution and computational cost: for copolymers, the number of distinguishable species grows exponentially with chain length. Quantum computing offers a potential alternative, provided the non-unitary rate matrices governing the kinetics can be embedded into unitary quantum circuits, a task known as block encoding. Here we construct explicit block-encoding circuits for two kinetic models of living polymerization: Model A, single-monomer polymerization, whose lower-bidiagonal rate matrix is encoded via a sparse-oracle construction and a two-term linear combination of unitaries (LCU) decomposition; and Model B, two-monomer copolymerization, where a bijective labeling of polymer species by an integer index (the m-index) yields a structured sparse matrix encoded via either a five-term LCU or a sparse-oracle construction. Numerical simulations with the sparse-oracle encodings reproduce the classical time evolution for reactivity ratios drawn from reported olefin copolymerization systems spanning near-random ($r_1 r_2 \simeq 1$) and blocky ($r_1 r_2 > 1$) microstructures, and the LCU encodings are verified by explicit reconstruction of the encoded matrix block. Resource estimation shows that both implementations require only $O(\log N)$ qubits in the matrix dimension $N$ (an exponential memory saving over the classical state space), with gate counts growing gradually, reaching $10^4$ to $10^5$ gates at $10^3$ system qubits. These results establish a concrete quantum circuit foundation for simulating polymerization kinetics on fault-tolerant quantum hardware, and a first step toward exploiting exponential state-space compression for high-dimensional polymer reaction networks.
发表机构
- QunaSys Inc.（QunaSys公司）
- Graduate School of Informatics, Nagoya University（名古屋大学大学院信息学研究科）
机构由 AI 辅助整理，请以论文原文为准。
