AI 中文总结
针对量子计算流体动力学中非线性项的实现瓶颈，本文提出混合量子-经典张量网络算法，通过张量块编码稳定成功概率，在湍流模拟中降低了内存与计算成本，为量子优势的实现提供了可扩展路径。
AI 中文摘要
非线性项是量子计算流体动力学面临的核心挑战，因为在本质上线性的量子硬件上实现这些项通常需要资源密集型的变通方案，这限制了其向大规模模拟的可扩展性。我们提出一种混合量子-经典张量网络算法，通过结合变分时间步长与量子张量编程，将算子和时变场高效编译为量子电路，以此解决这一瓶颈。在概率框架内，我们用基于张量的块编码取代了先前基于状态的非线性实现，稳定了原本会随系统大小指数衰减的成功概率。对湍流流场的基准测试表明，该算法在雷诺数和网格分辨率不断提高的情况下，仍能保持高成功概率和适度的测量开销。与纯经典张量网络求解器相比，我们的混合方法在内存占用和计算成本上均实现了大幅降低，为尺度解析计算流体动力学（CFD）模拟中实用量子优势的实现建立了可扩展路径。
英文摘要
Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations.
Comments16 pages, 8 figures
