Grant: Discovery Grants Program - Individual

This theoretical research program is designed to study light-matter interfaces for scalable photonic quantum information processing and to develop efficient characterization and quantum control tools for scalable quantum processing devices. The main goals are I) quantum non-linear optics for developing non-classical sources and for photonic quantum simulation, II) efficient quantum process tomography for characterizing and benchmarking scalable quantum processing devices, and III) quantum control for engineering light-matter interfaces for quantum optical signal processing. Achieving nonlinear interaction between pulses of light at the single photon level will enable entangling gates between optical photons. The Rydberg interaction between atoms is a promising approach towards quantum nonlinear optics. This is now being considered with individually trapped atoms to simulate complex quantum systems and to solve problems in computing science such as maximum independent set. This research program will develop theoretical models and numerical tools to study the Rydberg physics in atoms and bound states of excitons in semiconductors to create non-classical sources of photons for photonic quantum computation and to develop methods for quantum simulation in these systems. Quantum state and process tomography provide the experimental recipe and mathematical groundwork to deduce quantum states and characterize quantum processes. This has been used to characterize and benchmark quantum experiments and devices. However, both quantum state and process tomography require an exponential number of measurements to reconstruct density or process matrix of a 2n-dimensional system of n qubits. Due to the increasing computational cost of the reconstruction procedure, it is not possible to characterize large-scale quantum systems. In this research program, we plan to develop scalable tools in quantum tomography. This will be driven by including prior knowledge of the quantum state and processing devices; for example the class of quantum states or the topology of the device. The results will be extremely valuable in characterizing future quantum computing devices. The third research direction of this program will pursue development of quantum control techniques to engineer quantum light-matter interfaces for novel quantum optical information processing tasks. For example, engineering spectral features in quantum memories will enable quantum signal processing operations such as bandwidth modulation, add-drop filtering, and temporal signal sequencing. Specifically, we will focus our approach on designing light-matter interfaces based on rare-earth ion-doped crystals for processing optical signals where optical hole-burning is used to prepare absorption features. The result of this research direction will guide our experimental collaborators to extend functionalities of these devices to take a step closer in developing elements of large-scale quantum networks.