Can a quantum computer run the von Neumann architecture?

Abstract

At the core of nearly every modern computer is a central processing unit running the von Neumann architecture. This computer architecture gives computationally universal machines, and non-trivial control structures arise naturally, leading to high-level programming constructs. At the core of the von Neumann architecture is the notion that program code may be stored and manipulated in the same way as data. A datum describing an operation may be stored and processed in the same way as any other form of data, but may also be 'promoted' to an operation, and applied. Classically, this is well-studied-particularly from a categorical point of view. We consider such operations in the quantum setting, including Nielsen and Chuang's orthonormal encoding, Abramsky and Coecke's categorical foundations, the BBC protocol, and the Choi-Jamiołkowsky correspondence. Obstacles to a quantum analogue of the von Neumann architecture are also considered, including the no-cloning and no-deleting theorems, the "no-programming principle", and the Gottesman-Knill theorem. © 2010 Springer-Verlag Berlin Heidelberg.