On the fundamental level, quantum fluctuations or entanglement lead to complex dynamical behaviour in many-body systems¹ for which a description as emergent phenomena can be found within the framework of quantum field theory. A central quantity in these efforts, containing all information about the measurable physical properties, is the quantum effective action². Though non-equilibrium quantum dynamics can be exactly formulated in terms of the quantum effective action, finding solutions is in general beyond the capabilities of classical computers³. Here, we present a strategy to determine the non-equilibrium quantum effective action⁴ using analogue quantum simulators, and demonstrate our method experimentally with a quasi-one-dimensional spinor Bose gas out of equilibrium^5,6. Spatially resolved snapshots of the complex-valued transversal spin field⁷ allow us to infer the quantum effective action up to fourth order in an expansion in one-particle irreducible correlation functions at equal times. We uncover a strong suppression of the irreducible four vertex emerging at low momenta in the highly occupied regime far from equilibrium where perturbative descriptions fail⁸. Our work constitutes a new realm of large-scale analogue quantum computing⁹, where highly controlled synthetic quantum systems¹⁰ provide the means for solving theoretical problems in high-energy and condensed-matter physics with an experimental approach^11,12,13,14.

从根本上讲，量子涨落或纠缠会导致多体系统^1发生复杂的动力学行为，在量子场论的框架内可以找到对这种现象的描述。在这些工作中，包含有关可测量的物理性质的所有信息的中心量是量子有效作用²。尽管可以根据量子有效作用来精确地制定非平衡量子动力​​学，但是找到解决方案通常超出了传统计算机的能力³。在这里，我们提出一种确定非平衡量子有效作用的策略⁴使用模拟量子模拟器，并用准一维自旋玻色子气体进行了实验，证明了我们的方法不平衡^5,6。复数值横向自旋场^7的空间分辨快照使我们能够在相等时间的单粒子不可约相关函数的展开中推断量子有效作用直至四阶。我们发现，在高占位状态下，在低动量处出现的不可约的四个顶点受到强烈抑制，而远离扰动描述失败的平衡状态⁸。我们的工作构成了大规模模拟量子计算的新领域⁹，其中高度受控的合成量子系统¹⁰通过实验方法^11,12,13,14提供解决高能和凝聚态物理理论问题的方法。