Research Projects

The design and control of quantum states of many degrees of freedom with desired symmetry, topology, and information-theoretic features, characterized by quantum entanglement, are currently at the forefront of research in condensed matter physics and quantum technology. Quantum computers, e.g., made of many superconducting qubits, are also complex quantum many-body systems. However, unlike conventional solid-state systems, these many-body assemblies, while evolving under various unitary gate operations, can also be frequently monitored by an external observer through repeated quantum measurements and feedback. Thus, quantum computers are specific types of open quantum systems, where the repeated monitoring can be used as an engineered bath, in addition to usual sources of environmental dissipation and decoherence. Given the practical and fundamental relevance of the topic, there has been a surge of theoretical and experimental activities on the control and manipulation of quantum states by measurements and bath engineering in open quantum systems in many-body physics. For example, measurement-induced entanglement phase transitions (MIEPTs) have led to a new paradigm of dynamical phase transitions. MIEPTs are curious transitions between distinct phases of non-equilibrium steady states (NESSs), arsing due to competition between repeated disentangling measurements and entangling unitary evolution of quantum many-body systems. Apart from realizing MIEPTs, an extensive number of measurements, when performed once or a few times, can alter the nature of quantum many-body ground states and transform simple initial states into ones with non-trivial symmetry and topology. However, standard experiments probe the state of the monitored systems by averaging over many possible measurement outcomes, and repeated measurements typically lead to a featureless steady state, on average. A much richer structure of even the averaged steady states, e.g., with symmetry breaking or non-trivial topology, can be attained in a monitored system when measurements are complemented with quantum feedback. The interplay of monitoring with unitary dynamics, symmetry, topology, and entanglement in quantum systems with many degrees of freedom leads us to fascinating and rather uncharted territory of quantum many-body physics. To this end, the proposal has two major goals: (1) to study how measurements and feedback can be used to design and manipulate quantum many-body states and characterize their quantum-information-theoretic properties like entanglement, and (2) to explore non-equilibrium statistical mechanics of monitored systems. To achieve the above goals, the proposed project (i) will develop theoretical formalisms and methods to describe non-unitary time evolution of monitored systems of fermions, bosons, and spins. These methods will involve both analytical and numerical quantum many-body physics frameworks. (ii) Approximate and/or exact numerical techniques within these frameworks will be used to study dynamical phase transitions like MIEPT by computing entanglement properties of the monitoring-induced states. (iii) We will explore the role of feedback to control symmetry-breaking topological properties and entanglement structure of monitored systems. (iv) We will address fundamental questions regarding non-equilibrium statistical physics of monitored systems, e.g., the notion of thermalization, statistical ensemble, and fluctuation-dissipation relation of states obtained through monitoring. (v) We will study the possibility of realizing the monitored dynamics in realistic Josephson-junction (JJ) based qubit systems and microwave cavity quantum electrodynamics setup, which are one of the most promising platforms for quantum computing. Such realizations can pave the way to control and manipulate quantum states and understand the many-body physics of quantum computers.

Quantum measurements, Quantum feedback, Quantum entanglement, Monitored dynamics, Many-body physics