AI 中文总结
研究人员在量子处理器上首次实验实现非线性时间传播，采用混合变分框架处理伯格斯方程，通过量子-经典优化重构随时间变化的场，为非线性连续动力学的量子计算开辟了新途径。
AI 中文摘要
从流体流动、输运到集体动力学，非线性偏微分方程的数值模拟是现代科学计算的基础。将这一能力扩展到量子计算机仍是长期挑战，因为非线性和非厄米演化与基于哈密顿量的传统量子模拟根本不兼容。本文中，我们在量子处理器上实验实现了非线性流体动力学的时间演化，采用混合变分框架处理粘性和无粘性伯格斯方程。我们的方法将非线性动力学直接编码到变分优化过程中，避免了基于卡莱曼线性化的量子算法相关的扩大线性嵌入和截断开销。我们进一步演示了对应雷诺数约为10²的对流主导动力学。我们将控制演化编码到参数化量子电路中，通过量子-经典优化迭代重构随时间变化的场。通过引入无额外电路折叠开销的零噪声外推方法，我们准确执行了纠缠门数量超出哈达玛测试电路典型值的深层误差电路。尽管存在硬件噪声和有限的器件相干性，我们仍在多个时间步上准确重构了时间演化。据我们所知，我们的结果构成了量子处理器上非线性时间传播的首次实验实现，将量子模拟扩展到主要线性设置之外，为非线性连续动力学的量子计算建立了一条途径。
英文摘要
From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $10^2$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.
Comments13 pages, 5 figures
