  Quantum theory, originally proposed as a physical theory to describe the
motions of microscopic particles, has been applied to various non-physics
domains involving human cognition and decision-making that are inherently
uncertain and exhibit certain non-classical, quantum-like characteristics.
Sentiment analysis is a typical example of such domains. In the last few years,
by leveraging the modeling power of quantum probability (a non-classical
probability stemming from quantum mechanics methodology) and deep neural
networks, a range of novel quantum-cognitively inspired models for sentiment
analysis have emerged and performed well. This survey presents a timely
overview of the latest developments in this fascinating cross-disciplinary
area. We first provide a background of quantum probability and quantum
cognition at a theoretical level, analyzing their advantages over classical
theories in modeling the cognitive aspects of sentiment analysis. Then, recent
quantum-cognitively inspired models are introduced and discussed in detail,
focusing on how they approach the key challenges of the sentiment analysis
task. Finally, we discuss the limitations of the current research and highlight
future research directions.
