Dynamical topological phases in monitored quantum circuits

建议的博士项目属于凝聚态理论的研究领域。该项目致力于探索凝聚态和量子科学的动态交集，利用量子信息中的概念，如凝聚态物理领域的纠缠熵和量子复杂性。随着我们见证创新的NISQ时代多体系统的到来，包括里德伯格原子阵列和其他数字量子计算机，使用凝聚态物理的工具来理解这些系统变得势在必行。这一领域的一个关键观察结果是，由酉门构成的量子电路表现出测量诱导的相变，这种相变可以用非厄米哈密顿量来描述。这一至关重要的见解为实现本质上非厄米特的“点间隙”拓扑铺平了道路--这是一种在量子电路领域内对物质的动力学相进行创新的范例，没有平衡对应物。这个博士项目的主要重点是通过在真实世界的量子模拟器上进行严格的测试来系统地建立和验证这种对应关系。随后要追求的研究途径是基于对称性和拓扑学对量子电路的动力学相进行分类。该项目融合了凝聚态物理和量子计算的学科，雄心勃勃的目标是使用近期的量子硬件来实现物质的动力学相，而平衡相不存在。学生将负责建立一个强大的理论框架，同时还将在量子模拟器上执行实际实验。该项目有明确的起点和明确的后续研究目标。除了解决一个悬而未决的问题，这项研究还有可能描绘出工程量子系统中的紧急现象，从而有望立即应用于实际。这些应用可能包括开发新颖的、受凝聚态启发的量子算法，例如用于组合优化或量子化学。该项目还将促进帝国理工学院专门从事量子科学和凝聚态理论的团队之间富有成效的合作，并培育一个富有成效的跨学科学术环境。

The proposed Ph.D. project lies in the research area of condensed matter theory. The project endeavors to explore the dynamic intersection of condensed matter and quantum science, leveraging concepts from quantum information such as entanglement entropy and quantum complexity in the realm of condensed matter physics. As we witness the advent of innovative NISQ-era many-body systems, including Rydberg atom arrays and other digital quantum computers, it becomes imperative to comprehend these systems using the tools from condensed matter physics. A key observation in this field has been that quantum circuits constructed from unitary gates exhibit measurement-induced phase transitions, which can be aptly described through non-Hermitian Hamiltonians. This crucial insight paves the way for the realization of intrinsically non-Hermitian "point gap" topology-an innovative paradigm for dynamical phases of matter, devoid of equilibrium counterparts, within the sphere of quantum circuits. The primary focus of this Ph.D. project is to systematically establish and validate this correspondence through rigorous testing on real-world quantum simulators. A subsequent research avenue to be pursued entails the classification of dynamical phases of quantum circuits based on symmetry and topology. The project amalgamates the disciplines of condensed matter physics and quantum computing, with an ambitious aim to actualize dynamical phases of matter, absent in equilibrium counterparts, using near-term quantum hardware. The student will be responsible for establishing a robust theoretical framework while also executing practical experiments on quantum simulators. The project has a definitive inception point and clear successive research objectives. In addition to resolving an open problem, the research holds potential for mapping out emergent phenomena in engineered quantum systems, thereby promising immediate practical applications. These applications could include the development of novel, condensed matter inspired quantum algorithms e.g. for combinatorial optimization or quantum chemistry. The project will also galvanize a productive collaboration between the groups at Imperial specializing in quantum science and condensed matter theory and foster a fruitful interdisciplinary academic environment.