Probability for Deep Learning Quantum

Probability for Deep Learning Quantum: A Many-Sorted Algebra View provides readers with the first book to address probabilistic methods in the deep learning environment and the quantum technological area simultaneously, by using a common platform: the Many-Sorted Algebra (MSA) view. While machine learning is created with a foundation of probability, probability is at the heart of quantum physics as well. It is the cornerstone in quantum applications. These applications include quantum measuring, quantum information theory, quantum communication theory, quantum sensing, quantum signal processing, quantum computing, quantum cryptography, and quantum machine learning. Although some of the probabilistic methods differ in machine learning disciplines from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, in Komogorov's vision. It is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. This algebraic construct is also used in showing the shared structures underlying much of both machine learning and quantum theory. Both deep learning and quantum technologies have several probabilistic and stochastic methods in common. These methods are described and illustrated using numerous examples within the text. Concepts in entropy are provided from a Shannon as well as a von-Neumann view. Singular value decomposition is applied in machine learning and as a basic tool in the Schmidt decomposition. Reproducing Kernel Hilbert Spaces (RKHS) are introduced in the text for use in support vector machines as well as in Tikhonov Regularization methods. In quantum, the Bargmann-Fock Space is one of the many RKHS. Besides the in-common methods, Born's rule as well as positive operator valued measures are described and illustrated, along with quasi-probabilities. Author Charles R. Giardina provides clear and concise explanations, accompanied by insightful visualizations and thought-provoking exercises, to deepen your understanding and enable you to apply the concepts to real-world scenarios.