Quantum simulation of far-from-equilibrium gauge-theory dynamics

我目前工作的主要主题是围绕规范理论的非平衡动力学和量子模拟，规范理论是具有局域规范对称性的基本量子多体模型，通过物质和规范场之间的局域约束来编码自然规律。实现规范理论的大规模量子模拟器并稳定和控制它们的失衡动力学是一个突出的挑战，它的完成将允许在可访问的桌面量子设备上探索一些最基本的自然界问题。特别是，我对两个方面感兴趣：(I)理解并在技术上利用这些模型的非平衡动力学，因为这些模型与高能和凝聚态物理都相关，(Ii)通过严格的理论框架在现代量子模拟器上设计规范理论的受控和可靠的实现。尽管在这两个方面取得了令人印象深刻的进展，但仍然存在重大悬而未决的问题。在第一方面，这些问题包括规范理论中的热化或缺乏热化，禁闭-解禁闭转变，更高空间维度中的弦断裂，规范理论中无序局域化的性质及其与正统多体局域化的关系，量子多体伤痕的规范理论起源，阶梯预热化及其与高斯定律的动力学重整化的联系，仅举几例。对这些问题的研究对于我们更好地理解量子多体模型，特别是规范理论是如何脱离平衡的，并具有促进量子信息技术应用的前景，具有重要的基础意义。在第二方面，尽管取得了令人印象深刻的进展，但在规范理论的量子模拟方面仍有很多工作要做。虽然重要的原理验证实验已经证明了在小的积木上模拟规范对称性，但对超越最简单的规范群的动力学物质耦合的规范场的大规模模拟仍然有待实施。规范理论的圣杯，具有SU(3)非阿贝尔规范对称性的量子色动力学，要在现实的大规模量子模拟器上实现，仍然有很长的路要走。致力于规范理论模拟的量子模拟器具有超越经典方法的真正潜力，因此发展这项技术具有重要意义。

The main subject of my current work is concentrated around the out-of-equilibrium dynamics and quantum simulation of gauge theories, which are fundamental quantum many-body models with local gauge symmetries that encode the laws of nature through local constraints between matter and gauge fields. Achieving large-scale quantum simulators of gauge theories and stabilizing and controlling their out-of-equilibrium dynamics is an outstanding challenge whose accomplishment will allow probing some of the most fundamental questions of nature on accessible table-top quantum devices. In particular, I am interested in two fronts: (i) understanding and technologically leveraging the out-of-equilibrium dynamics of these models as relevant to both high-energy and condensed matter physics, and (ii) devising controlled and reliable realizations of gauge theories on modern quantum simulators through rigorous theoretical frameworks. Although there has been impressive progress on these two fronts, there are still major open questions. On the first front, these include thermalization or lack thereof in gauge theories, the confinement-deconfinement transition, string breaking in higher spatial dimensions, the nature of disorder-free localization in gauge theories and its relation to orthodox many-body localization, the gauge-theoretic origin of quantum many-body scars, staircase prethermalization and its connection to the dynamical renormalization of Gauss's law, to name a few. Research into these questions is of fundamental importance in allowing us to better understand how quantum many-body models in general, and gauge theories in particular, behave out of equilibrium, and has the promising prospect of facilitating applications in quantum information technologies. On the second front, despite impressive progress, there remains a lot to do in terms of the quantum simulation of gauge theories. While important proof-of-principle experiments have demonstrated the simulation of gauge symmetries on small building blocks, large-scale simulations of gauge fields coupled to dynamical matter beyond the simplest gauge groups remain to be implemented. The holy grail of gauge theories, quantum chromodynamics with its SU(3) non-Abelian gauge symmetry, is still a long way to implement on a realistic large-scale quantum simulator. Quantum simulators dedicated to the simulation of gauge theories have the real potential to surpass classical methods, and therefore advancing this technology is of great significance.