Recursive quantum repeater networks

Internet-scale quantum repeater networks will be heterogeneous in physical technology, repeater functionality, and management. The classical control necessary to use the network will therefore face similar issues as Internet data transmission. Many scalability and management problems that arose during the development of the Internet might have been solved in a more uniform fashion, improving flexibility and reducing redundant engineering effort. Quantum repeater network development is currently at the stage where we risk similar duplication when separate systems are combined. We propose a unifying framework that can be used with all existing repeater designs. We introduce the notion of a Quantum Recursive Network Architecture, developed from the emerging classical concept of 'recursive networks', extending recursive mechanisms from a focus on data forwarding to a more general distributed computing request framework. Recursion abstracts independent transit networks as single relay nodes, unifies software layering, and virtualizes the addresses of resources to improve information hiding and resource management. Our architecture is useful for building arbitrary distributed states, including fundamental distributed states such as Bell pairs and GHZ, W, and cluster states.Comment: 14 page

Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many figure