PART II: Modern Applications
Quantum Information Science
4.1 QUANTUM BITS AND TENSOR PRODUCTS
Quantum information science is an interdisciplinary subject that includes physics, mathematics, chemistry, electrical engineering, and computer science, and has the potential to revolutionize many areas of science and technology. It exploits fundamentally new modes of computation and information processing, because it is based on the laws of quantum mechanics instead of those of classical physics. It holds the promise of immense computing power beyond the capabilities of any classical computer, and it is directly linked to emerging quantum technologies, such as quantum teleportation. The key element of quantum information science is a quantum system with two states that can represent “0” and “1,” the basic building blocks of a digital logic circuit called “qubit.” A qubit is a unit vector in a two-dimensional Hilbert space, whose basis vectors (computational basis) are defined as 
In order to implement any useful quantum information processing unit, we need to deal with many qubits at a time, and the appropriate model is a tensor product of qubits. Specifically, if we have n qubits, each with a given computational basis in a two dimensional Hilbert space , then the tensor product ...