Dynamical topological phases in monitored quantum circuits

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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.