State Transfer on Graphs
Chris Godsil

TL;DR
This paper surveys mathematical research on perfect state transfer in graphs, a quantum computing concept involving the operator exp(itA) and specific vertex transfer conditions.
Contribution
It provides a comprehensive overview of mathematical results related to perfect state transfer in graphs, highlighting key developments and open questions.
Findings
Summary of conditions for perfect state transfer
Identification of graph classes with perfect state transfer
Discussion of mathematical techniques used in the field
Abstract
If is a graph with adjacency matrix , then we define to be the operator . We say that we have perfect state transfer in from the vertex to the vertex at time if the -entry of . This concept has potential applications in quantum computing. We offer a survey of some of the work on perfect state transfer and related questions. The emphasis is almost entirely on the mathematics.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
