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The Illinois Express Quantum Network (IEQNET) is a program to realize metropolitan-scale quantum networking over deployed optical fiber using currently available technology. IEQNET consists of multiple sites that are geographically dispersed in the Chicago metropolitan area. Each site has one or more quantum nodes (Q-Nodes) representing the communication parties in a quantum network. Q-Nodes generate or measure quantum signals such as entangled photons and communicate the measurement results via standard classical signals and conventional networking processes. The entangled photons in IEQNET nodes are generated at multiple wavelengths and are selectively distributed to the desired users via transparent optical switches. Here, we describe the network architecture of IEQNET, including the Internet-inspired layered hierarchy that leverages software-defined networking (SDN) technology to perform traditional wavelength routing and assignment between the Q-Nodes. Specifically, SDN decouples the control and data planes, with the control plane being entirely implemented in the classical domain. We also discuss the IEQNET processes that address issues associated with synchronization, calibration, network monitoring, and scheduling. An important goal of IEQNET is to demonstrate the extent to which the control plane classical signals can copropagate with the data plane quantum signals in the same fiber lines (quantum-classical signal “coexistence”). This goal is furthered by the use of tunable narrowband optical filtering at the receivers and, at least in some cases, a wide wavelength separation between the quantum and classical channels. We envision IEQNET to aid in developing robust and practical quantum networks by demonstrating metropolitan-scale quantum communication tasks such as entanglement distribution and quantum-state teleportation.