Capturing the meaning of sentences has long been a challenging task. Current models tend to apply linear combinations of word features to conduct semantic composition for bigger-granularity units e.g. phrases, sentences, and documents. However, the semantic linearity does not always hold in human language. For instance, the meaning of the phrase `ivory tower' can not be deduced by linearly combining the meanings of `ivory' and `tower'. To address this issue, we propose a new framework that models different levels of semantic units (e.g. sememe, word, sentence, and semantic abstraction) on a single \textit{Semantic Hilbert Space}, which naturally admits a non-linear semantic composition by means of a complex-valued vector word representation. An end-to-end neural network~\footnote{https://github.com/wabyking/qnn} is proposed to implement the framework in the text classification task, and evaluation results on six benchmarking text classification datasets demonstrate the effectiveness, robustness and self-explanation power of the proposed model. Furthermore, intuitive case studies are conducted to help end users to understand how the framework works.
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