Designing Optimal Multi-Photon Measurement-Assisted Entangling Transformations for Quantum Information Processing

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Embedding and processing information at the elementary quantum level creates a new physical paradigm for a family of revolutionary technologies. These range from quantum algorithms, which place public-key cryptography at risk, to the exponential speedup of quantum chemistry codes for applications in nanophysics. Currently the field of quantum information is passing from the phase of conceptual development and 'proof of principle' laboratory experiments to the building of physical devices capable of performing simple computational, communicational, and metrological tasks. Compared to other physical implementations, encoding and transmission of quantum information in quantum states of light exploits extremely low photon decoherence rates. Therefore, quantum photonics is considered as a constituent part of future quantum information devices. Since photons as elementary particles are non-interacting, building a linear optical device capable of entangling individual photons has become a challenging theoretical task. It requires the development of efficient numerical and analytical tools for optimization of measurement-assisted transformations in exponentially large Hilbert spaces of multi-mode and multi-photon states, including photonic cluster states for one-way quantum computation. The main body of the research consists of two interrelated topics: (1) Optimization of measurement-assisted multi-photon gates. The focus is on developing efficient numerical schemes for optimization of fidelity and success probability of quantum transformations on photonic qubits. Methods recently proposed and implemented for two-qubit gates will be applied to three- and four-qubit transformations, cluster fusion gates, and multi-qubit error-correction operations. (2) Error correction in optical realizations of quantum communication and quantum computation. The goal is to adapt the abstract theory of quantum error correction to the experimentally relevant problem of photon loss in quantum communication. The objective is to find optical circuits that realize error correction tasks and are simple enough to be implemented in experiment, such as recently suggested error-correction codes using hyper-entangled photonic states. This work also has immediate extension to the optimization of error-correcting codes for continuous-variable quantum systems.This project enhances research opportunities for undergraduate and graduate students through direct stipend support, professional development through travel to conferences, and active participation in external collaborations with quantum information research groups at Louisiana State University, the University of Illinois, McGill University, and the University of Queensland. The participation of under-represented groups will be significantly broadened by strengthening links with Xavier University of Louisiana, a major historically African American institution in New Orleans, as well as by bringing in talented minority undergraduates through the Louis Stokes Louisiana Alliance for Minority Participation (LS-LAMP) program. Outreach and teaching will be supported through interdisciplinary seminars on quantum mechanics for first-year non-major students and liberal arts physics courses, and at the upper undergraduate and graduate levels through new course offerings on quantum information and quantum computing that are being developed at Tulane. Finally, research collaboration between the two major research universities in Louisiana will be enhanced, by building on existing cooperation between new Division of Physical and Materials Sciences at Tulane and the Hearne Institute for Theoretical Physics at LSU.