for hard computational problems; (2) characterize the efficiency of candidate quantum algorithms; and (3) develop insights into the power of quantum computation and consider issues of quantum complexity and computability.Proposals for research in quantum algorithms should primarily be to devise specific quantum algorithms to solve mathematically and computationally hard problems from such diverse fields as algebra, number theory, geometry, analysis, optimization, graph theory, differential equations, combinatorics, topology, logic, and simulation. Quantum algorithms that are developed should focus on constructive solutions for specific tasks and on general methodologies for expressing and analyzing algorithms tailored to specific problems. Complexity analyses such as upper and lower bounds on algorithms relative to specific models of quantum computation are also encouraged. Proposals may be submitted by degree-granting universities (foreign and domestic), nonprofit organizations, or industrial concerns (large and small businesses). Proposals are encouraged from Historically Black Colleges and Universities (as determined by the Secretary of Education to meet requirements of Title III of the Higher Education Act of 1965, as amended (20 U.S.C. §1061) and from Minority Institutions defined as institutions whose enrollment of a single minority or a combination of minorities exceeds 50 percent of the total enrollment. [20 U.S.C. § 1067k(3) and 20 U.S.C. § 2323(a)(1)(C)]. However, no funds are specifically allocated for HBCU/MI participation.Awards made under this BAA may be in the form of contracts or grants and are subject to the availability of appropriations. Multi-year projects must have clear goals for each year. Funding for subsequent years will be contingent upon satisfactory performance and the availability of funds.Multiple, one to three year awards are anticipated. The maximum total of any award is five (5) years. Most proposals will request less than $200K per year. Larger proposals that combine the efforts of multiple investigators from multiple institutions will be considered if a strong and compelling case is made for such a combined effort, rather than multiple smaller efforts.