Towards Photonic Non-Abelian Quantum Gates

量子信息科学是在过去几十年里兴起的一个领域，它解决了这样一个问题：通过存储、处理和传输内在量子力学系统中编码的信息来利用量子力学效应，是否可以导致新的现象、功能和设备。量子信息既是基础科学又是新技术的先驱。光子量子系统提供了许多优点，从低水平的退相干到精确的单粒子量子控制，并且是可移动的。激光写入集成光子波导提供了独特的能力，设计复杂，稳定的量子信息电路，具有前所未有的灵活性。例如，与非阿贝尔合成规范油田相关的非阿贝尔几何相位最近已成功实现。这些相位对于拓扑量子计算、非阿贝尔任意子统计和杨-米尔斯理论的量子模拟至关重要。我们的建议的目的是促进光子非阿贝尔U(N)完整体在集成波导架构中的实现，并为在噪声中尺度量子（NISQ）处理框架中的新量子信息处理应用奠定基础。特别地，在提议的项目中，我们将(1)发展U(3)完整的理论基础，并通过实验证明使用两个不可区分的光子和四个耦合点的网络，其中波导的弯曲几何已被优化；(2)开发和演示一个概念和实验框架，包括我们集成波导电路功能中的非正交模式和非绝热量子态演化，这将使我们能够访问更大的简并子空间，包括两个光子的U(4)-完整，以及(3)实现各种完整量子门并实验演示完整量子计算协议。我们的提案的优势在于结合两个非常富有成果的现代研究方向：多光子态操纵和集成光电路，以探索量子信息处理的基本概念，促进基础科学和光子应用的发展。

Quantum information science, a field that has emerged over the past several decades, addresses the question of whether harnessing quantum mechanical effects through storing, processing and transmitting information encoded in inherently quantum mechanical systems can lead to new phenomena, functionalities, and devices. Quantum information is both fundamental science and a progenitor for new technologies. Photonic quantum systems provide many advantages, reaching from low levels of decoherence to precise single-particle quantum control and being mobile. Laser-written integrated photonic waveguides provide the unique capability of designing complex, stable quantum information circuitry with unprecedented flexibility. For example, non-Abelian geometric phases associated with non-Abelian synthetic gauge fields have recently been successfully implemented. Such phases are crucial for topological quantum computation, non-Abelian anyon statistics, and the quantum simulation of Yang–Mills theories. The aim of our proposal is to promote the implementation of photonic non-Abelian U(N) holonomies in integrated waveguide architectures with the vision to establish a basis for new quantum information processing applications in the framework of noisy intermediate-scale quantum (NISQ) processing. In particular, in the proposed project we will (1) develop the theoretical foundations for and experimentally demonstrate a U(3) holonomy using two indistinguishable photons and a network of four coupled sites, in which the waveguides’ bending geometry has been optimized, (2) develop and demonstrate a conceptual and experimental framework to include non-orthogonal modes and non-adiabatic quantum state evolution in the functionality of our integrated waveguide circuits which will allow us to access larger degenerate subspaces, including a U(4)-holonomy for two photons, and (3) implement various holonomic quantum gates and experimentally demonstrate holonomic quantum computation protocols. The strength of our proposal comes from combining two very fruitful modern research directions: multi-photon-state manipulation and integrated optical circuitry in order to explore fundamental concepts of quantum information processing, for the advancement of fundamental science as well as photonic applications.