ABSTRACT

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.

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