Quantum Cross Entropy and Maximum Likelihood Principle

Machine learning has attracted interests from various fields as a powerful tool in finding patterns in data. Supported by machine learning technology, computer programs can improve automatically through experience, which has enabled a wide spectrum of applications: from visual and speech recognition, effective web search, to study of human genomics [1, 2]. Classical machine learning techniques have also found many interesting applications in different disciplines of quantum physics [3, 4, 5, 6, 7, 8, 9, 10]. With the advancement of quantum information science and technology, there are both theoretical and practical interests in understanding quantum systems, building quantum devices, developing quantum algorithms, and ultimately, taking advantages of quantum supremacy [11, 12].