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We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical… (More)

Let K be a full-dimensional convex subset of R n. We describe a new polynomial-time Turing reduction from the weak separation problem for K to the weak optimization problem for K that is based on a geometric heuristic. We compare our reduction, which relies on analytic centers, with the standard, more general reduction.

It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively… (More)

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