Theory of Computing addresses the problem of understanding the fundamental nature and limits of computation. Algorithms addresses the problem of how to best solve specific problems using minimal time and space resources.
Quantum Computing addresses the problem of how to compute using quantum mechanical phenomenon, such as photons.Specific problems in the Theory of Computing include how to classify problems as to their degree of difficulty. Specific problems in Algorithms include finding (optimal) algorithms for computing problems, and proving that a given problem requires a certain minimum amount of resources for its solution. Specific problems in Quantum Computing include finding algorithms for solving problems efficiently using quantum information.