Classical computation with quantum systems

Abstract

As semiconductor electronic devices scale to the nanometer range and quantum structures (molecules, fullerenes, quantum dots, nanotubes) are investigated for use in information processing and storage, it becomes useful to explore the limits imposed by quantum mechanics on classical computing. To formulate the problem of a quantum mechanical description of classical computing, electronic device and logic gates are described as quantum sub-systems with inputs treated as boundary conditions, outputs expressed as operator expectation values, and transfer characteristics and logic operations expressed through the sub-system Hamiltonian, with constraints appropriate to the boundary conditions. This approach, naturally, leads to a description of the sub-systems in terms of density matrices. Application of the maximum entropy principle subject to the boundary conditions (inputs) allows for the determination of the density matrix (logic operation), and for calculation of expectation values of operators over a finite region (outputs). The method allows for an analysis of the static properties of quantum sub-systems.