Sparse Uniformly Coupled Networks
By Kevin
Introduction
A quantum network can be modeled as a graph, with vertices representing sites that can hold an excitation and edges representing couplings between those sites. An excitation may be spread across several sites in a superposition. As the state evolves, probability amplitudes combine through interference, changing where the excitation is likely to be found [1]. Adding a connection can therefore help or hurt transfer. Since each coupling also takes work to implement and calibrate, we have a reason to examine networks with relatively few edges.
We will investigate how connectivity affects the probability of transferring an excitation between two sites within a fixed time. Starting with minimally connected networks, we will compare the best transfer available when one or two additional edges are allowed. We will also measure what happens when a single edge is added to a particular network while the source–target distance stays the same. We will examine every small network in our stated range, then use a heuristic search to explore larger networks.
Intellectual Merit
Previous research has studied how to achieve reliable state transfer with limited network resources [2, 3]. Our project will compare transfer under four constraints, namely the number of sites, the number of extra edges, the source–target distance, and the available time. This comparison will help distinguish the benefit of generally higher edge density from the effect of placing an edge in a particular location. Our results will factor in improvements, decreases, and negligible differences in transfer across graphs.
Broader Impact
Our project aims to produce a database of small networks, with their transfer probabilities and the code used to calculate them. Future research groups could use these results to choose networks for further study or check their own simulations. Documenting the analysis and its limits will make our work easier to reproduce and build off of.