**May 13-14, 2019**

**University of Arizona, College of Optical Sciences**

**Tucson, AZ**

May 13-14, University of Arizona, Tucson

The United States National Research Council defines network science as “the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena.”

Network science is discipline that studies complex networks that may appear in telecommunication networks, computer networks, biological networks, cognitive and semantic networks, neural networks, statistical thermodynamics of interacting particles, co-authorship networks, and other forms of social networks. They consider elements or actors represented by nodes (or vertices, or site) and connections between the elements as links (or edges, or bonds). The field draws on theories and methods including graph theory (from mathematics), statistical mechanics (from physics), data mining and information visualization (from computer science), inferential modeling (from statistics), and social structure (from sociology).

Networks involving quantum mechanical elements or actors are called *quantum networks*. Quantum networks are even richer than their classical counterparts with regards to their various properties. This is due to the fact that quantum nodes can be in superposition states, and pairs (or groups) of nodes can be entangled.

The goal of this 2-day workshop is to explore a new discipline “Quantum Network Science”, in analogy to (classical) network science, which would aim at developing unifying mathematical principles behind large complex quantum-correlated many-body networks, to explore their structural and dynamic properties, characterization, evolution and manipulation of multi-site entanglement, and their applications in quantum communications, sensing, simulations and computation.

Large complex quantum networks emerge in condensed matter systems, in certain biological systems, in high energy physics, in cluster-model quantum computing, to perhaps an engineered quantum internet of the future.

We would like to bring together people with intersections of the following expertise:

(1) **complex networks **(emergent behavior in large networks, network measures such as centrality, dynamic networks, robustness, …)

(2) **mathematical statistics** (percolation theory, large deviations, critical exponents, …)

(3) **quantum information theory** (quantum Shannon theory, capacity of multi-user channels, quantum error correction, …)

(4) **network theory** (computer networks, routing and resource allocation, latency-throughput tradeoffs, network performance measures, …)

(5) **quantum networks** (quantum repeaters, multipath and multiflow routing of entanglement, quantum network coding, …)

(6) **quantum computing** (cluster states, distributed quantum computing)

The workshop will be sub-divided into the following topics. The detailed organization (talks, discussions, breakouts, etc.) will be announced and communicated to the attendees soon.

**Topic 1 **Properties of complex quantum networks

**Topic 2: **Entanglement in a large quantum network

**Topic 3:** Dynamical properties of many-body quantum systems

**Topic 4: **Cluster model quantum computing

**Topic 5:** Experimental realizations of quantum networks