Towards scalable quantum information processing and quantum networks

这一理论研究计划旨在研究用于可扩展光子量子信息处理的光-物质界面，并开发用于可扩展量子处理设备的高效表征和量子控制工具。主要目标是i)用于开发非经典源和用于光子量子模拟的量子非线性光学，ii)用于表征和基准可扩展量子处理设备的高效量子过程层析成像，以及iii)用于量子光信号处理的工程光-物质界面的量子控制。 在单光子水平上实现光脉冲之间的非线性相互作用将使光学光子之间的纠缠门成为可能。原子间的里德堡相互作用是一种很有前途的量子非线性光学方法。现在正在考虑用单独捕获的原子来模拟复杂的量子系统，并解决计算科学中的问题，如最大独立集。这项研究计划将开发理论模型和数值工具，以研究原子中的里德堡物理和半导体中激子的束缚态，创建用于光子量子计算的非经典光子源，并开发这些系统中的量子模拟方法。 量子态和过程层析成像为推导量子态和表征量子过程提供了实验配方和数学基础。这已经被用来描述量子实验和设备的特征和基准。然而，量子态和过程层析成像都需要指数数量的测量来重建2n维n量子比特系统的密度或过程矩阵。由于重建过程的计算成本增加，不可能表征大规模的量子系统。在这个研究项目中，我们计划开发可扩展的量子断层扫描工具。这将通过包括量子态和处理设备的先验知识来驱动；例如，量子态的类别或设备的拓扑。这一结果将对描述未来的量子计算设备具有极其重要的价值。 本计划的第三个研究方向是追求量子控制技术的发展，以 为新的量子光学信息处理任务设计量子光-物质接口。例如，量子存储器中的工程频谱功能将使量子信号处理操作成为可能，如带宽调制、分插滤波和时间信号排序。具体地说，我们将重点设计基于稀土离子掺杂晶体的光-物质界面，用于处理光学信号，其中光学烧孔用于制备吸收特性。这一研究方向的结果将指导我们的实验合作者扩展这些设备的功能，从而在开发大规模量子网络的元素方面更近一步。

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.