Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in mind, envisioning standalone applications. However, near-term quantum computers are susceptible to noise which limits their standalone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This {it modus operandi} calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR, that enables single-source quantum-classical programming. Programs written using the QCOR library and directives based language extensions can be compiled to produce functional hybrid binary executables. After defining the QCORs programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed forward quantum computing. QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high performance computing (HPC). The high level of abstraction in the developed language is intended to accelerate the adoption of quantum computing by researchers familiar with classical HPC.
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