1,197,956 research outputs found
The world problem: on the computability of the topology of 4-manifolds
Topological classification of the 4-manifolds bridges computation theory and
physics. A proof of the undecidability of the homeomorphy problem for
4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary
Turing machine with an arbitrary input can be encoded into the topology of a
4-manifold, such that the 4-manifold is homeomorphic to a certain other
4-manifold if and only if the corresponding Turing machine halts on the
associated input. Physical implications are briefly discussed.Comment: Submitted to Class. Quant. Gra
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
- …