A unified approach to quantum computation and classical reversible computation

The design of a quantum computer and the design of a classical computer can be based on quite similar circuit designs. The former is based on the subgroup structure of the infinite group of unitary matrices, whereas the latter is based on the subgroup structure of the finite group of permutation matrices. Because these two groups display similarities as well as differences, the corresponding circuit designs are comparable but not identical

On Orthogonal Band Allocation for Multi-User Multi-Band Cognitive Radio Networks: Stability Analysis

In this work, we study the problem of band allocation of $M_s$ buffered secondary users (SUs) to $M_p$ primary bands licensed to (owned by) $M_p$ buffered primary users (PUs). The bands are assigned to SUs in an orthogonal (one-to-one) fashion such that neither band sharing nor multi-band allocations are permitted. In order to study the stability region of the secondary network, the optimization problem used to obtain the stability region's envelope (closure) is established and is shown to be a linear program which can be solved efficiently and reliably. We compare our orthogonal allocation system with two typical low-complexity and intuitive band allocation systems. In one system, each cognitive user chooses a band randomly in each time slot with some assignment probability designed such that the system maintained stable, while in the other system fixed (deterministic) band assignment is adopted throughout the lifetime of the network. We derive the stability regions of these two systems. We prove mathematically, as well as through numerical results, the advantages of our proposed orthogonal system over the other two systems.Comment: Conditional Acceptance in IEEE Transactions on Communication