RAISE:TAQS: High Dimensional Frequency Bin Entanglement -- Photonic Integration and Algorithms

纠缠是一种基本的量子力学现象，其中粒子的波函数是相关的，使得它们不可分割的状态必须被写为相干叠加，是量子信息处理（QIP）的关键资源。典型的QIP系统基于两能级量子态，也称为量子位。然而，基于qudits（量子信息的高维单位）的高维系统比最常探索的传统二维量子比特系统有几个潜在的优势，包括每个粒子更高的信息容量和更强的抗噪声能力。本文主要研究高维光子纠缠的频率自由度，也称为双光子频率梳（bfc）。拟议的项目旨在推进用于量子信息处理的频率编码光子的科学和技术。这个项目应该为培养学生提供很好的机会。技术：这个高度跨学科的项目将在许多方面推进知识。(1)对高维BFC光子的相干性和纠缠性进行严格的验证，是未来频率盒编码光子应用的基础。(2)提出的光子集成工作可能导致一种新型的量子芯片，用于高维BFC态的生成、制备、测量和处理。与之前的离散元件工作相比，集成光子学的实现可以导致更低的损耗，这对于扩展到更复杂或级联操作以及演示更高维度的纠缠至关重要。(3)与量子比特相比，使用量子位的量子计算算法尚未得到充分探索。该项目将产生新的量子模拟方法，寻求利用高维（qudit）编码来有效地表示具有高维自由度的复杂多体系统，例如描述由电子/激子模式和振动模式之间耦合产生的极化子/极化子准粒子的霍尔斯坦哈密顿量。(4)该团队将使用光子硬件设计并执行概念验证实验，以实现所开发量子算法的选定方面。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Entanglement, a fundamentally quantum mechanical phenomenon in which the wave functions of particles are correlated such that their inseparable states must be written as coherent superpositions, is akey resource for quantum information processing (QIP). Typical QIP systems are based on two-levelquantum states, also called qubits. However, high-dimensional systems based on qudits (highdimensional units of quantum information) have several potential advantages over the conventional two-dimensional qubit systems most commonly explored, including higher information capacity per particleand stronger immunity to noise. This proposal focuses on high dimensional photon entanglement in the frequency degree of freedom, also referred to as biphoton frequency combs (BFCs). The proposed project seeks to advance the science and technology of frequency-encoded photons for quantum information processing. This project should provide excellent opportunities for training of students.Technical: This highly interdisciplinary project will advance knowledge in many fronts. (1) Rigorous certification of coherence and entanglement in high dimensional BFC photons is fundamental to the future application of frequency-bin encoded photons. (2) The proposed photonic integration effort could lead to a new class of quantum chips architected for generation, preparation, measurement, and processing of high dimensional BFC states. Compared to prior work with discrete components, implementation in integrated photonics can lead to much lower losses, which is critical to scaling to more complex or cascaded operations and to demonstrating entanglement in even higher dimensions. (3) Algorithms for quantum computation using qudits have been underexplored compared to their qubit counterparts. This project will produce new quantum simulation methodologies that seek to exploit high dimensional (qudit) encoding for efficient representation of complex many-body systems with high dimensional degrees of freedom, such as the Holstein Hamiltonian describing polaron/polariton quasiparticles resulting from the coupling between electronic/excitonic modes and vibrational modes. (4) The team will design and perform proof-of-concept experiments using photonic hardware to realize selected aspects of the developed quantum algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.