This is an exciting time for quantum computing where early-stage quantum computers become available at your fingertips through clouds. The conventional design of quantum algorithms is centered around the abstraction of quantum circuits and relies on a digital mindset for application design and implementation. While serving as an elegant mathematical interface, circuit-based digital abstraction usually fails to capture the native programmability of quantum devices, and incurs large overheads, which significantly restricts its near-term feasibility where the quantum computing resource is the major limitation. 

We propose to use quantum Hamiltonian evolution as the central object in end-to-end quantum application design, i.e. the so-called Hamiltonian-oriented paradigm, based on the observation that Hamiltonian evolution is a native abstraction for both low-level hardware control and high-level quantum applications. We illustrate that the Hamiltonian-oriented design not only allows more efficient implementation of existing quantum algorithms but also inspires novel quantum algorithms, especially in optimization and scientific computing, which are hard to perceive in the circuit model. We also develop a programming infrastructure called SIMUQ (SIMUlation language for Quantum) for easy implementation of Hamiltonian-based quantum applications for domain experts on heterogeneous quantum devices.