Quantum Computing and Quantum Simulation in the Optical Frequency Comb

寻求全功能、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·费曼最先提出的那样，一台运行中的量子计算机将带来革命性的进步，它将使量子计算达到目前深不可测的规模。生物大分子就是一个例子，它可以以前所未有的方式推动药物发现。量子计算机的另一个重要应用是Shor的算法，该算法对整数进行指数分解，速度比经典计算机快，这将提供一种方法来击败当前的标准加密方法(如RSA)，因此与国家安全相关。实现量子计算是一项难度极大的任务，理想的实验平台尚不清楚。阻碍实现实际规模的量子计算机的两个令人生畏的挑战是克服退相干，即使可靠的量子比特成为量子比特，并实现可伸缩性，即产生大量可单独寻址的量子比特。在全球范围内，相互竞争的方法涉及电磁陷阱中的离子、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。在NSF的支持下，弗吉尼亚大学的量子场和量子信息(QFQI)小组成功地开发了最后一种方法。它建立在利用光谱编码密度的基础上，可用于宽带发射激光器，更准确地说，是光学参量振荡器(OPO)。这个项目致力于在一个超紧凑的物理系统中实现量子信息和量子计算的独特、可扩展的实现：由单个OPO的共振模式(Qumodes)定义的量子光学频率梳。在NSF的支持下，QFQI小组提出了这个想法，并在实验室中率先实施，展示了多体纠缠的创纪录水平(60 Qumodes，量子比特的光场模拟)，并与悉尼大学的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间域，并使用频率-时间混合纠缠，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伸缩的二维正方形网格格子簇态，通过将频域和时间纠缠结合起来-因为频率和时间将有效地构成正方形网格格子的每个维度，该状态仍然将发生在单个OPO中。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最近证明了该方案存在容错阈值。

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.