Quantum networks are at the center of recent advances in quantum information, communication, and computation. These networks can be used to simulate complex materials and study the emergence of order in many-body systems. To explore new capabilities on the frontiers of engineered coherent matter that these systems might provide, the National Academies of Sciences, Engineering, and Medicine Condensed Matter and Materials Research Committee held a hybrid in-person and online workshop in Washington, DC on October 3, 2024. The workshop reviewed the rapidly emerging implementations of these systems and their relation to fundamental problems and applications in condensed matter physics, materials science, and quantum information. This publication summarizes the presentations and discussion of the workshop.