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The current paradigm of scientific computing relies on Moore’s law, which has enabled more sophisticated models, bigger problem sizes, and finer resolutions. However, even with a continuous growth of computing power, many multi-scale and multi-physics problems will remain inaccessible. It is often speculated that quantum computing may bring the desired game-changing capabilities. However, there is a wide gap between promised quantum advantages on fault-tolerant computers versus what is achievable on near-term devices. Our research bridges the gap between what is possible in principle and what is achievable in practice by developing quantum algorithms and realizing them on hardware. On the algorithm side, because quantum computers rely on unitary operations instead of logic gates, efficient quantum algorithms need to be designed differently than their classical counterparts. We also design algorithms to simulate intrinsically quantum problems that are hopeless for classical computers, but may become feasible for quantum computers. On the hardware side, different platforms have their unique limitations and advantages, which need to be balanced when compiling quantum programs for execution. Our research takes an algorithm-hardware co-design approach to ensure that quantum algorithms are grounded with hardware realities, while enabling applications that may shape the maturation of future quantum technologies.