Designing Optimal Multi-Photon Measurement-Assisted Entangling Transformations for Quantum Information Processing

在基本量子水平上嵌入和处理信息，为一系列革命性技术创造了一种新的物理范式。这些问题包括将公钥密码术置于危险境地的量子算法，以及用于纳米物理应用的量子化学代码的指数加速。目前，量子信息领域正在从概念开发和“原理证明”的实验室实验阶段过渡到能够执行简单的计算、通信和计量任务的物理设备的构建阶段。与其他物理实现相比，在光的量子态中编码和传输量子信息利用了极低的光子退相干速率。因此，量子光子学被认为是未来量子信息器件的组成部分。由于光子作为基本粒子是不相互作用的，因此建立一个能够纠缠单个光子的线性光学装置已经成为一个具有挑战性的理论任务。这就需要开发有效的数值和分析工具来优化指数级大的多模和多光子希尔伯特空间中的测量辅助变换，包括用于单向量子计算的光子簇态。研究的主体由两个相互关联的主题组成：(1)测量辅助多光子门的优化。重点是开发高效的数值方案来优化光子量子比特上的量子变换的保真度和成功概率。最近提出和实现的两个量子比特门的方法将被应用于三个和四个量子比特变换、集群融合门和多量子比特纠错操作。(2)量子通信和量子计算的光学实现中的纠错。其目标是使量子纠错的抽象理论适用于量子通信中与实验相关的光子损失问题。其目标是找到实现纠错任务并且足够简单以便在实验中实现的光学电路，例如最近提出的使用超纠缠光子态的纠错码。这项工作还立即扩展到连续变量量子系统的纠错码优化。该项目通过直接津贴支持，通过参加会议进行专业发展，以及积极参与与路易斯安那州立大学、伊利诺伊大学、麦吉尔大学和昆士兰大学的量子信息研究小组的外部合作，为本科生和研究生增加研究机会。通过加强与路易斯安那州泽维尔大学的联系，以及通过路易斯安那州少数族裔参与联盟(LS-LAMP)计划引进有才华的少数族裔本科生，将大大扩大代表不足群体的参与范围。将通过为一年级非主修学生和文科物理课程举办关于量子力学的跨学科研讨会，并通过杜兰大学正在开发的关于量子信息和量子计算的新课程，在高年级本科生和研究生一级支持推广和教学。最后，将加强路易斯安那州两所主要研究型大学之间的研究合作，在杜兰新成立的物理和材料科学处与路易斯安那州立大学赫恩理论物理研究所之间现有合作的基础上再接再厉。

Embedding and processing information at the elementary quantum level creates a new physical paradigm for a family of revolutionary technologies. These range from quantum algorithms, which place public-key cryptography at risk, to the exponential speedup of quantum chemistry codes for applications in nanophysics. Currently the field of quantum information is passing from the phase of conceptual development and 'proof of principle' laboratory experiments to the building of physical devices capable of performing simple computational, communicational, and metrological tasks. Compared to other physical implementations, encoding and transmission of quantum information in quantum states of light exploits extremely low photon decoherence rates. Therefore, quantum photonics is considered as a constituent part of future quantum information devices. Since photons as elementary particles are non-interacting, building a linear optical device capable of entangling individual photons has become a challenging theoretical task. It requires the development of efficient numerical and analytical tools for optimization of measurement-assisted transformations in exponentially large Hilbert spaces of multi-mode and multi-photon states, including photonic cluster states for one-way quantum computation. The main body of the research consists of two interrelated topics: (1) Optimization of measurement-assisted multi-photon gates. The focus is on developing efficient numerical schemes for optimization of fidelity and success probability of quantum transformations on photonic qubits. Methods recently proposed and implemented for two-qubit gates will be applied to three- and four-qubit transformations, cluster fusion gates, and multi-qubit error-correction operations. (2) Error correction in optical realizations of quantum communication and quantum computation. The goal is to adapt the abstract theory of quantum error correction to the experimentally relevant problem of photon loss in quantum communication. The objective is to find optical circuits that realize error correction tasks and are simple enough to be implemented in experiment, such as recently suggested error-correction codes using hyper-entangled photonic states. This work also has immediate extension to the optimization of error-correcting codes for continuous-variable quantum systems.This project enhances research opportunities for undergraduate and graduate students through direct stipend support, professional development through travel to conferences, and active participation in external collaborations with quantum information research groups at Louisiana State University, the University of Illinois, McGill University, and the University of Queensland. The participation of under-represented groups will be significantly broadened by strengthening links with Xavier University of Louisiana, a major historically African American institution in New Orleans, as well as by bringing in talented minority undergraduates through the Louis Stokes Louisiana Alliance for Minority Participation (LS-LAMP) program. Outreach and teaching will be supported through interdisciplinary seminars on quantum mechanics for first-year non-major students and liberal arts physics courses, and at the upper undergraduate and graduate levels through new course offerings on quantum information and quantum computing that are being developed at Tulane. Finally, research collaboration between the two major research universities in Louisiana will be enhanced, by building on existing cooperation between new Division of Physical and Materials Sciences at Tulane and the Hearne Institute for Theoretical Physics at LSU.