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Error-bounded lossy compression has been a critical technique to significantly reduce the sheer amounts of simulation datasets for high-performance computing (HPC) scientific applications while effectively controlling the data distortion based on user-specified error bound. In many real-world use cases, users must perform computational operations on the compressed data. However, none of the existing error-bounded lossy compressors support operations, inevitably resulting in undesired decompression costs. In this paper, we propose a novel error-bounded lossy compressor (called SZOps), which supports not only error-bounding features but efficient computations (including negation, scalar addition, scalar multiplication, mean, variance, etc.) on the compressed data without the complete decompression step, which is the first attempt to the best of our knowledge. We develop several optimization strategies to maximize the overall compression ratio and execution performance. We evaluate SZOps compared to other state-of-the-art lossy compressors based on multiple real-world scientific application datasets.