空间变输运-反应方程量子模拟的资源分析
Resource Analysis for Quantum Simulation of Spatially Varying Transport-Reaction Equations
AI总结：
本工作针对空间变输运-反应方程量子模拟的电路复杂度问题，分析采用稀疏FABLE块编码等方法构造的量子传播子的资源开销，为近期量子实现提供了实用估计。
AI中文摘要：
空间变系数是线性平流-扩散-反应方程量子模拟中电路复杂度的主要来源。本工作对采用稀疏FABLE块编码、量子奇异值变换及酉算子线性组合构造的单步量子传播子开展资源分析，根据空间离散化、稀疏性及多项式阶数推导量子比特数、门复杂度与电路深度的理论估计值，并将这些预测与一维、二维变系数问题的合成量子电路进行对比。所得分析量化了编码真实输运算子的成本，为近期实现提供了实用的资源估计。
英文摘要：
Spatially varying coefficients are the primary source of circuit complexity in quantum simulation of linear advection-diffusion-reaction equations. This work presents a resource analysis of single-step quantum propagators constructed using sparse FABLE block encodings, Quantum Singular Value Transformation, and linear-combination-of-unitaries. We derive theoretical estimates for qubit count, gate complexity, and circuit depth in terms of the spatial discretization, sparsity, and polynomial degree, and compare these predictions with synthesized quantum circuits for one- and two-dimensional variable-coefficient problems. The resulting analysis quantifies the cost of encoding realistic transport operators and provides practical resource estimates for near-term implementations.
