发表机构
University College London（伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于局域约化密度矩阵代价函数的变分时间演化原理，通过局域优化矩阵乘积态实现量子多体系统的有效模拟，并在量子硬件上验证了其恢复局域动力学的能力。
AI 中文摘要
多体动力学中的传统量子优势基于避免在经典计算机上模拟的代价，这种代价源于全局波函数广泛的指数复杂性。然而，局域可观测量并不继承这种广泛的复杂性，反而可能由与系统总大小无关的内在局域复杂性所支配。这一区别在热化系统中尤为重要，因为局域可观测量会失去微观细节的记忆，并弛豫到仅由少数参数决定的平衡值。这里我们引入一个变分时间演化原理，通过用定义在局域约化密度矩阵上的代价函数替代全局态保真度来利用这一区别。由此产生的演化保留了相干的短时动力学，同时利用了后期热化带来的简化。我们提出的具体算法基于局域优化矩阵乘积态，并允许类似于含时变分原理的闭式运动方程。我们证明相同的变分原理具有量子-经典对应物，将局域代价的量子评估与对测量噪声和硬件噪声均稳健的优化策略相结合。在Quantinuum H2和IBM Heron处理器上的原理验证实现恢复了特征性的局域动力学。
英文摘要
Conventional quantum advantage in many-body dynamics is based on avoiding the simulation cost on a classical computer that arises from the extensive exponential complexity of the global wavefunction. Local observables, however, do not inherit this extensive complexity and may instead be governed by an intrinsic local complexity that is independent of the total system size. This distinction is particularly relevant in thermalising systems, where local observables lose memory of microscopic details and relax towards equilibrium values determined by only a few parameters. Here we introduce a variational time-evolution principle that exploits this distinction by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting evolution retains coherent short-time dynamics while exploiting the simplification produced by thermalisation at later times. The concrete algorithm we propose is based on locally optimising matrix-product states and admits closed-form equations of motion analogous to the time-dependent variational principle. We show that the same variational principle has a quantum-classical counterpart, combining quantum evaluation of the local cost with an optimisation strategy robust to both shot and hardware noise. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.
Comments18 pages, 12 figures
