New Linear-Optical Approach to Quantum Information Processing and Quantum Simulation

Deepesh Singh

John Calsamiglia

Yuta Okubo

雄太 大久保

Shuto Osawa

The progress in modern quantum information processing (QIP) strongly depends on new algorithms and on the development of novel quantum entanglement processing elements enabling to perform quantum computation and quantum simulation effectively. Several examples of quantum information processing applications based on freshly designed linear-optics devices are presented. A beam splitter (BS) is a central device in linear-optical quantum information processing because it can split the incoming photon amplitudes into spatially distinct modes to establish conditions for quantum superposition. The BS naturally possesses directional-bias in a sense that incoming photons can only propagate in a forward manner. When the execution of certain quantum information tasks would require multiple operations, this directionality condition becomes a serious obstacle by creating significant overhead in the number of needed elements and other supporting devices. We introduce a family of amplitude-controllable fully-reversible linear-optical quantum information processors, called directionally-unbiased linear-optical multiports, in order to achieve significant reduction in the number of required hardware. The theoretical analysis of the device design as well as the experimental realization of three-port unit using bulk linear optics is demonstrated. These devices offer several fresh approaches in quantum-walk-based applications such as quantum simulation of solid-state Hamiltonians, topological protection of polarization qubits against errors, and quantum communication. Topological photonics is an emerging and actively developing field because of its capability to stabilize and protect some quantum states from perturbation errors by ensuring the environment carries a distinct topological signature. Topology-dependent quantum information processing is globally stable due to the entire system being engaged in the information manipulation. We demonstrate suppression of quantum amplitude transfer between two distinct bulk regions of a system. This results in error avoidance for a two-photon polarization-entangled state under specific conditions. The goal of modern quantum communication is a reliable distribution of quantum entanglement between multiple nodes performing quantum operations such as quantum memories and quantum computers. We demonstrated that local quantum information processing using new fully-reversible four-port linear-optical structures could find an immediate application in quantum communication. A quantum information routing device is introduced based on the use of four-dimensional Grover matrices and beam splitters. Several multiport-based units are developed to demonstrate new higher-dimensional Hong-Ou-Mandel (HOM) effect and directionally-controllable entangled state distribution while changing only phases in a waveguided unit. Several such operational elements could be linked to form a reconfigurable network of quantum users without losing control of quantum amplitudes. This allows controllable routing of entangled photons and sharing entanglement between any designated users in the future quantum computational networks.

Casey A. Fitzpatrick

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). \nMany important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. \n \nIn this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. \n \nFinally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.