There are many design problems need to be optimized in various fields of engineering, and most of them belong to the NP-hard problem. The meta-heuristic algorithm is one kind of optimization method and provides an effective way to solve the NP-hard problem. Salp swarm algorithm (SSA) is a nature-inspired algorithm that mimics and mathematically models the behavior of slap swarm in nature. However, similar to most of the meta-heuristic algorithms, the traditional SSA has some shortcomings, such as entrapment in local optima. In this paper, the three main strategies are adopted to strengthen the basic SSA, including chaos theory, sine-cosine mechanism and the principle of quantum computation. Therefore, the SSA variant is proposed in this research, namely SCQ-SSA. The representative benchmark functions are employed to test the performances of the algorithms. The SCQ-SSA are compared with the seven algorithms in high-dimensional functions (1000 dimensions), seven SSA variants and six advanced variants on benchmark functions, the experiment reveals that the SCQ-SSA enhances resulting precision and alleviates local optimal problems. Besides, the SCQ-SSA is applied to resolve three classical engineering problems: tubular column design problem, tension/compression spring design problem and pressure vessel design problem. The design results indicate that these engineering problems are optimized with high accuracy and superiority by the improved SSA. The source code is available in the URL: https://github.com/ye-zero/SCQSSA/tree/main/SCQ-SSA.