Probability for Deep Learning Quantum is the first book to address probabilistic methods in the deep learning environment and the quantum technology field simultaneously, using a common platform: the Many-Sorted Algebra (MSA) view. Probability is the foundation of machine learning and it is the heart of quantum physics as well. It is indeed the cornerstone of quantum applications, which 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 in machine learning disciplines differ from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, using Komogorov's axioms. The treatment is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. This algebraic construct is also used in show the shared structures underlying much of both machine learning and quantum theory. 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 and von-Neumann viewpoints. Singular value decomposition is applied in machine learning as a basic tool and presented in the Schmidt decomposition. Besides the methods in common, 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 and thought-provoking visualizations, to deepen your understanding and enable you to apply the concepts to real-world scenarios. Key Feautures: Provides hundreds of well-crafted examples illustrating the difficult concepts pertaining to quantum and stochastic processes, Addresses probabilistic methods in the deep learning environment and quantum technology field. Presents the algebraic underpinning of both quantum and deep learning rigorously and precisely.