面向混合量子-高性能计算系统的、内存、电路与本征态拟设高效的变分量子线性求解器（VQLS）用于计算流体动力学（CFD）
Memory-, Circuit-, and Ansatz-Efficient VQLS for CFD on Hybrid Quantum-HPC Systems
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中文总结 AI 辅助
本研究针对混合量子-HPC系统上VQLS用于CFD的三大挑战，通过基准测试编码策略、评估本征态拟设、在Frontier超算部署工作流，建立了实用基线并明确了更大规模问题的瓶颈。
中文摘要 AI 辅助
流体动力学工作负载主要由大型结构化线性系统的重复求解主导，这推动了对量子加速的探索。变分量子线性求解器（VQLS）是近期有前景的候选方案，但在混合量子-高性能计算（HPC）系统上的实际部署面临三个持续存在的挑战：（i）系统矩阵的幺正线性组合（LCU）编码会随问题规模增大而导致内存和运行时间爆炸；（ii）本征态拟设（ansatz）的选择在很大程度上是经验性的，标准电路指标与求解器收敛性之间没有明确关联；（iii）端到端VQLS流程很少在具有非平凡量子比特数的生产级HPC硬件上运行。本研究通过三项贡献解决这些挑战：首先，我们对四种矩阵编码策略进行基准测试——朴素LCU、集成PennyLane的、基于快速沃尔什-哈达玛变换（FWHT）的并行泡利分解，以及基于奇异值分解（SVD）的两项式LCU——结果显示，在11×11的Hele-Shaw网格上，FWHT方法将峰值内存降低了多达1298倍，而基于SVD的相干VQLS在8量子比特下比标准泡利型VQLS实现了超过10000倍的每迭代加速；其次，我们在经典Hele-Shaw流上评估了11种本征态拟设族，结合无梯度和基于梯度的优化器，发现表达能力和纠缠度量与VQLS收敛性仅存在弱相关性，这催生了面向特定问题的本征态拟设设计；第三，我们将完整工作流程部署在OLCF Frontier超级计算机上，并在单个节点上成功模拟了15量子比特的三对角托普利茨系统。这些结果共同为混合量子-HPC计算流体动力学（CFD）工作流中的VQLS建立了实用基线，并确定了更大规模问题的剩余瓶颈。
英文摘要
Fluid dynamics workloads are dominated by repeated solves of large, structured linear systems, motivating the search for quantum acceleration. The Variational Quantum Linear Solver (VQLS) is a leading near-term candidate, but practical deployment on hybrid quantum--high--performance computing (HPC) systems faces three persistent challenges: (i) the linear-combination-of-unitaries (LCU) encoding of the system matrix explodes in memory and runtime as the problem size grows, (ii) ansatz selection is largely empirical, with no clear link between standard circuit metrics and solver convergence, and (iii) end-to-end VQLS pipelines have rarely been exercised on production HPC hardware at non-trivial qubit counts. This work addresses these challenges through three contributions. First, we benchmark four matrix-encoding strategies---naive LCU, PennyLane-integrated, Fast Walsh--Hadamard Transform (FWHT)-based parallel Pauli decomposition, and an singular value decomposition (SVD)-based two-term LCU---and show that the FWHT approach reduces peak memory by up to $1298\times$ on an $11\times 11$ Hele--Shaw grid, while the SVD-based coherent VQLS delivers over $10{,}000\times$ per-iteration speedup over standard Pauli-based VQLS at 8 qubits. Second, we evaluate 11 ansatz families with gradient-free and gradient-based optimizers on canonical Hele--Shaw flow, and find that expressibility and entanglement metrics correlate only weakly with VQLS convergence, motivating problem-aware ansatz design. Third, we deploy the full workflow on the OLCF Frontier supercomputer and successfully simulate a 15-qubit tridiagonal Toeplitz system on a single node. Together, these results establish a practical baseline for VQLS in hybrid quantum--HPC computation fluid dynamic (CFD) workflows and identify the remaining bottlenecks for larger problems.
