Quantum Computing and Quantum Simulation in the Optical Frequency Comb

追求功能齐全、通用的量子计算是一个重要的科学和社会目标。正如理查德·费曼（Richard Feynman）首次提出的那样，一台工作的量子计算机将带来革命性的进步，使量子计算能够在目前深不可测的尺度上实现。大型生物分子就是一个例子，它可以以前所未有的方式促进药物发现。量子计算机的另一个重要应用是肖尔算法，它可以比传统计算机以指数速度分解整数，这将提供一种击败当前标准加密方法（如RSA）的方法，因此与国家安全相关。量子计算的实现是一项极其艰巨的任务，理想的实验平台目前还不知道。实现实用量子计算机的两个艰巨挑战是克服退相干，即制造可靠的量子比特“量子位”和实现可扩展性，即产生大量可单独寻址的量子位。在世界范围内，与之竞争的方法包括电磁陷阱中的离子、光学陷阱中的原子、超导电路、人造原子（如量子点）或钻石中的工程掺杂空位缺陷，以及纯光。最后一种方法在美国国家科学基金会的支持下，由弗吉尼亚大学的量子场和量子信息（QFQI）小组成功开发。它建立在利用可用于宽带发射激光器的光谱编码密度的基础上，更准确地说，是光学参量振荡器（OPO）。该项目解决了超紧凑物理系统中量子信息和量子计算的独特可扩展实现：由单个OPO的谐振模式（qumodes）定义的量子光学频率梳。在美国国家科学基金会的支持下，QFQI小组提出了这个想法，并率先在实验室中实施，展示了创纪录水平的多部纠缠（60个量子模，量子比特的光场类似物），并与悉尼大学的尼克·梅尼库奇（Nick Menicucci）合作获得了几个理论结果。该项目将把这种广泛成功的频域纠缠方法扩展到时域，并使用混合频率-时间纠缠，以便在单个OPO中实现通用量子计算机。这将需要首次实现完全可扩展的二维方形网格-晶格簇状态，这仍然会发生在单个OPO中，通过结合频域和时域纠缠，因为频率和时间将有效地构成方形网格的每个维度。这种实现包括使用Gottesman-Kitaev-Preskill方案进行量子错误编码的可能性，Menicucci最近证明了容错阈值的存在。

The quest for fully functional, universal quantum computing is an important scientific and societal goal. A working quantum computer would bring about revolutionary advances by enabling quantum calculations at currently unfathomable scales, as first proposed by Richard Feynman. An example would be that of large biological molecules, which could empower drug discovery in an unprecedented manner. Another important application for the quantum computer is provided by Shor's algorithm for factoring integers exponentially faster than a classical computer, which would provide a way to defeat the current standard encryption methods (such as RSA) and is hence of relevance to national security. The realization of quantum computing is an inordinately difficult task for which the ideal experimental platform is not yet known. The two daunting challenges that stand in the way of the realization of a practical quantum computer of nontrivial size are overcoming decoherence, i.e., making reliable quantum bits 'qubits' and achieving scalability, i.e., producing large numbers of individually addressable qubits. Competing approaches on a worldwide scale involve ions in electromagnetic traps, atoms in optical traps, superconducting circuits, artificial atoms such as quantum dots or engineered dopant-vacancy defects in diamond, and pure light. The last approach has been successfully developed, with NSF support, by the Quantum Fields and Quantum Information (QFQI) group at the University of Virginia. It builds on exploiting the density of spectral encoding available to braodband emitting lasers and, more precisely, optical parametric oscillators (OPO). This project addresses a unique, scalable implementation of quantum information and quantum computing in an ultracompact physical system: the quantum optical frequency comb defined by the resonant modes (qumodes) of a single OPO. With NSF support, the QFQI group initiated the idea and pioneered its implementation in the laboratory, demonstrating record-levels of multipartite entanglement (60 qumodes, the optical field analogs of qubits) and obtaining several theoretical results in collaboration with Nick Menicucci at the U. of Sydney. The project will expand this widely successful frequency-domain entanglement approach to the time domain, and use hybrid frequency-time entanglement in order to implement a universal quantum computer in a single OPO. This will require the first ever realization of a fully scalable two-dimensional square-grid-lattice cluster state, which will still take place in a single OPO, by combining frequency-domain and time-domain entanglement --- as frequency and time will effectively constitute each dimension of the square-grid lattice. Such a realization includes the possibility of quantum error encoding using the Gottesman-Kitaev-Preskill scheme, for which Menicucci recently proved the existence of a fault tolerance threshold.