We live in a new Cambrian Explosion of hardware devices. The end of conventional processor scaling has driven research and industry practice to explore a new generation of approaches. The old DNA of architecture design, including vectors, threads, shared or private memories, coherence or message passing, dataflow or von Neumann execution, are hybridized together in new and exciting ways. Each new architecture exposes a unique hardware-level API. Performance and energy efficiency are critically dependent on how well programs can use these APIs. One approach is to implement custom libraries for each new hardware architecture and application domain. A more scalable approach is to utilize a portable compiler infrastructure tailored to the application domain that makes it easy to generate efficient code for a diverse set of architectures with minimal porting effort.We propose the Unified GraphIt Compiler framework (UGC), which does exactly this for graph applications. UGC achieves portability with reasonable effort by decoupling the architecture-independent algorithm from the architecture-specific schedules and backends. We introduce a new domain-specific intermediate representation, GraphIR, that is key to this decoupling. GraphIR encodes high-level algorithm and optimization information needed for hardware-specific code generation, making it easy to develop different backends (GraphVMs) for diverse architectures, including CPUs, GPUs, and next-generation hardware such as Swarm and the HammerBlade manycore. We also build scheduling language extensions that make it easy to expose optimization decisions like load balancing strategies, blocking for locality, and other data structure choices. We evaluate UGC on five algorithms and 10 input graphs on these 4 distinct architectures and show that UGC enables implementing optimizations that can provide up to 53× speedup over programmer-generated straightforward implementations.