Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis

Besides vectors, we also use the tensor product to construct operators in a larger space (more qubits) from smaller spaces (fewer qubits). We will practice the skill step-by-step that is clumsy but straightforward. Now with more qubits, it is possible that we only want to measure one or some of the qubits instead of all at once. This involves the concept of partial measurement that is important in many algorithms. Indeed, every type of qubit implementation needs to support partial measurement to be used in a quantum computer (DiVincenzo’s criteria). Finally, we will practice how to represent a matrix on a given basis to prepare us for advanced topics. At this step, we are done with the basics and linear algebra. We will start the exciting journey of quantum computing gates and algorithms in future chapters.