The Rise of the Boson-Sampling Quantum Computer and The Renaissance of the Linear Optical Quantum Interferometer

在长达20年的建造第一台量子计算机的竞赛中，已经研究了许多用于这种计算机的物理硬件平台，包括半导体电路、超导电路、在电磁芯片中操纵的带电离子原子，以及用激光控制的中性原子。一种落后的方法是设计一种使用光或光子的量子态的量子信息处理器。这是因为很难让光子相互作用或“交谈”，这是制造晶体管等量子计算元件的主要要求。在2010年前，基于光子的量子计算机电路设计在辅助量子和经典电路方面有巨大的开销，即使是建造一个简单的双光子晶体管也需要这样做。在一些早期的设计中，甚至需要数万个辅助光网络和电子开关来构建一个单光子晶体管。2010年，麻省理工学院的阿伦森·阿尔希波夫(Aaronson Arkhipov)展示了一种简单得多的光学电路--只用几个光子、透镜、镜子和其他简单的光学元件构成的线性光学干涉仪--可以用来解决一个特别困难的数学问题，处理能力比任何经典计算机都要高得多。从那时起，这种新型的光量子计算机已经在世界范围内进行了大约五次实验。对于这个项目，将研究这种新型简单光学计算机的不同电路设计，并将寻找它可能能够解决的其他数学问题。此外，还将研究使用这种简单的光学机器来制造成像设备(如显微镜)或传感器(如磁场传感器)的可能性，这些成像设备的操作分辨率、精确度和精确度比经典可能的更高。这个项目的巨大智力价值在于，它处于量子成像、传感和信息处理的界面上，所有这些都属于量子计量学领域。量子信息的语言提供了一个令人兴奋的工具，这样就可以使用在这些领域中的一个领域开发的工具来查看另一个领域的问题。因此，一个子领域的任何进步几乎都可以立即应用到另一个子领域，具有创造力和工作。这项工作是所有子领域的协同工作。所有参与这个项目的研究生和本科生都将接受量子力学、量子信息论、量子光学和AMO理论的基础培训。多模、被动、线性光学干涉仪用于量子计算、成像和传感的能力将具有广泛的跨学科商业、政府和科学影响。线性光学干涉仪一直被认为不适合于量子信息处理。虽然非线性干涉仪提供了一条通向可扩展和通用量子计算的途径，但实现这类方案所需的强烈光学非线性一直很难实现。即使是Knill，Laflamme和Milburn(KLM)提出的所谓线性光学量子计算(LOQC)方案也存在由检测和前馈过程产生的有效非线性。从技术角度来看，荷兰皇家航空公司的计划也被证明是令人望而生畏的，因为每个逻辑门需要大量的Ancilla资源。因此，当Aaronson和Arkhipov(AA)提出具有单光子输入的无源线性光学干涉仪可以有效地解决一类计算采样问题时，量子光学界感到惊讶，这个问题在经典甚至通用量子计算机上可能是难以解决的。这一结果引发了最近的一系列实验。道林的团队在研究具有多光子福克态输入的线性光学干涉仪中的量子随机游动时，得出了与AA类似的结论。综上所述，这些新的结果表明，简单的线性光学器件包含一种迄今被忽视的计算能力，这一能力才刚刚开始探索。路易斯安那州立大学已经开始从量子光学的角度研究这种设备的计算复杂性，使用标准的理论工具来描述光的量子态通过线性干涉仪的传播。除了为具有Fock态输入的器件的复杂性提供基本的量子光学论证外，还表明自发参数下转换光子源是一种可扩展的玻色子采样资源，并且与具有相干的广义猫态叠加的线性光学干涉仪的数目采样非常可能存在计算复杂性。(1)研究非高斯态输入(如光子加减态)下玻色子采样的计算复杂性；(2)对开发大规模后经典线性光学量子信息处理器的实际需求进行现实的资源分析；(3)研究具有高斯输入的非高斯(数分辨)采样的计算复杂性；(4)数值设计和测试小规模可编程的后经典量子信息处理器；(5)研究用于量子测量的线性光学干涉仪的性能，包括光学传感和成像。

In the twenty year long race to build the first quantum computer a number of physical hardware platforms for such a computer have been investigated including semiconductor circuits, superconducting circuits, charged ionic atoms manipulated in electromagnetic chips, and neutral atoms controlled with lasers. One approach that has lagged behind is the design of a quantum information processor that uses quantum states of light or photons. This is because it is difficult to get photons to interact or 'talk' to each other, a primary requirement in making quantum-computing elements such as transistors. Prior to 2010, photon-based quantum computer circuit designs had a huge overhead in the ancillary quantum and classical circuitry required to build even a simple two-photon transistor. In some of the early designs, tens of thousands of ancillary optical networks and electronic switches were required to construct even a single photon transistor. In 2010 Aaronson Arkhipov at MIT showed that much simpler optical circuit 'a linear optical interferometer' constructed with just a few photons, lenses, mirrors, and other simple optical elements, could be used to solve a particularly hard mathematical problem with an exponential increase in processing power over any classical computer. Since then some five experiments on this new type of optical quantum computer have been carried out worldwide. For this project different circuit designs of this new type of simple optical computer will be investigated and a search for additional mathematical problems that it might be able to solve will be carried out. In addition the possibility of using such a simple optical machine for making imaging devices such as microscopes, or sensors such as magnetic field sensors, that operate with more resolution, precision, and accuracy than is possible classically will be investigated. The great intellectual merit of this project is that it is at the interface of quantum imaging, sensing, and information processing all within the field of quantum metrology. The language of quantum information provides an exciting tool such that problems in one of these fields can be viewed using tools developed in another. Hence any advance in one subfield can almost immediately be applied, with creativity and work, to another subfield. The work is synergistic across all the subfields. All the graduate and undergraduate students involved in this project will be trained in the foundations of quantum mechanics, quantum information theory, quantum optics, and AMO theory. The power of multimode, passive, linear optical interferometers for quantum computation, imaging, and sensing will have broad cross-disciplinary commercial, governmental, and scientific impact.Linear optical interferometers have been thought to be unsuitable for quantum information processing. While nonlinear interferometers provide a route to scalable and universal quantum computation, the strong optical nonlinearities required to implement such schemes have been difficult to attain. Even the so-called linear optical quantum computing (LOQC) scheme proposed by Knill, Laflamme, and Milburn (KLM) has effective nonlinearities that are generated by the detection and feed-forward processes. The KLM scheme has also proved daunting from a technological standpoint due to the immense number of ancilla resources required per logical gate. It thus came as a surprise to the quantum optics community when Aaronson and Arkhipov (AA) proposed that passive linear optical interferometers with single photon inputs could efficiently solve a type of computational sampling problem, a problem that is likely intractable on a classical or even a universal quantum computer. This result has let to a flurry of recent experiments. Dowling's group was led to a similar conclusion as that of AA in the study of quantum random walks in linear optical interferometers with multiphoton Fock-state inputs. Taken together, these new results indicate that simple linear optical devices contain a hitherto overlooked computational capability that has only yet begun to be explored. LSU has begun an investigation of the computational complexity of such devices from a quantum optics point of view using the standard theoretical tools for describing the propagation of quantum states of lights through linear interferometers. In addition to providing an elementary quantum optical argument for the complexity of the devices with Fock-state inputs, it has been shown that spontaneous parametric down conversion photon sources are a scalable resource for boson sampling and that there is very likely a computational complexity associated with the number sampling of linear optical interferometers with superpositions of coherent 'generalized cat' states. The following tasks will be carried out: (1) investigate the computational complexity of boson sampling in the number basis with non-Gaussian state inputs such as photon added and subtracted Gaussian states; (2) carry out a realistic resource analysis of what is required in practice to develop a large-scale 'post-classical' linear optical quantum information processor; (3) investigate the computational complexity non-Gaussian (number-resolved) sampling with Gaussian inputs; (4) numerically design and test a small-scale programmable post-classical quantum information processor; (5) investigate the performance of linear optical interferometers for the purposes of quantum metrology including optical sensing and imaging.