The traditional representation of information uses bits, which can be in one of two states: 0 or 1. Quantum computing representation of information relies on qubits. A qubit or quantum bit can be in one of the two states, 0 or 1, but can also be a linear combination of both states.

*Quantum information science* is divided into four parts, and as the title suggests, it covers the topic of how information is represented using quantum mechanics principles.

Part 1 (chapters 1 through 5) covers the mathematical foundations of quantum computing: decision problems, computational models, linear algebra, and quantum mechanics. Although this part provides necessary background for the rest of the chapters, it is not a tutorial for complete beginners. Rather, it is a summary of the mathematical tools necessary to understand quantum information concepts.

Part 2 (chapters 6 through 8) discusses modern quantum mechanics, including density operators, quantum maps, and decoherence.

Part 3 (chapters 9 through 12) covers applications of quantum information science, namely entanglement, quantum algorithms, and different quantum simulations.

Part 4’s two chapters (13 and 14) focus on quantum engineering and the physics of superconducting devices.

*Quantum information science* is a comprehensive discussion of the field. Each chapter includes a further reading section, summary, and set of exercises with solutions. It is not meant for complete beginners though, as it requires a strong foundation in the related mathematics and physics.

The book is well written and logically organized. I would not recommend it as a tutorial on quantum information; however, as an advanced guide, practitioners can refer to it as needed. It can also be used in an advanced course on the subject.

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