This proposal targets a set of interdisciplinary tasks that directly address the challenges facing the burgeoning field of quantum information processing (QIP). In particular, both foundational work aimed at enhancing the understanding of fundamental underlying concepts, such as quan-tum entanglement, as well as applied work, such as designing quantum algorithms that would require only tens of qubits, while still providing better performance than their classical counter-parts, are targeted. The technical approaches to be adopted in the proposed work encompass a number of different fields, including quantum mechanics, quantum information theory and concepts, theory of computation, combinatorics, and classical electromagnetic fields and related computational methods. Intellectual Merits: A number of fundamental challenges need to be overcome before QIP can become a viable computing paradigm. This proposal addresses several of these challenges in a novel fashion, including: (i) What kinds of quantum algorithms can one implement in systems comprising tens of qubits? This is a very important issue facing the field of quantum computation: a system comprising the thousands of qubits necessary to factorize integers beyond the capability of existing classical computers is, at best, a long-term goal. In contrast, a system comprising tens of qubits is a conceivable goal; however, would there be any quantum algorithm that can be implemented on such a small scale computer and yet outperform classical algorithms? The proposal presents a quantum algorithm that can be used to simulate Maxwell's equations to determine classical electromagnetic mode frequencies of resonant structures, where the complete mode field distribution is not required. It is estimated that 50 logical qubits would be sufficient to produce useful electromagnetic simulation results. (ii) Is there life beyond Quantum Key Distribution? The proposal presents results where the basic tools of quantum cryptography are used to build a multi-participant protocol which gives the participants the ability to anonymously announce classical information. This protocol is shown to be secure against any and all attacks. This is the first ever multi-participant quantum protocol that uses a truly multipartite quantum entangled state. (iii) What are examples of nontrivial new quantum algorithms (i.e., other than Shor's factorization and Gover's search algorithms? The proposal reports results on the development of efficient quantum algorithms for determining the permanent of unitary and related matrices using the quantum optical model. A number of such critical open questions related to QIP are addressed. Broader Impacts: (i) Undergraduate Interdisciplinary Program: In collaboration with the Cal-ifornia Nano-science Institute (CNSI) and the Department of Electrical Engineering at UCLA, we are in the process of developing a nano-science interdepartmental program. Quantum in-formation processing is a key component of this program and the NSF grant will be leveraged to support this initiative, and in training graduate and undergraduate students. (ii) Annual Workshops On Quantum Information Processing: In collaboration with the NSF Institute of Pure and Applied Mathematics (IPAM) at UCLA, an interdisciplinary annual workshop on Quantum Information Processing and Computing will be held. (iii) Providing Support for Implementation-Oriented DARPA projects on Quantum Computing: Dr. Roychowdhury is the principal theoretician for a large interdisciplinary experimental group at UCLA working on de-veloping solid-state based quantum information processing technology. The experimental effort is currently supported by grants from DARPA and ARO, and the NSF grant will leverage the existing program and focus on transferring theoretical results to the experimental groups. (iv) Outreach and Minority Student Participation: Both IPAM and CNSI have institutional infras-tructures in place to attract minority and K12 students, and we plan to engage them and train them through seminars and free access to our workshops.
