We start with a formal description of quantum computation. Quantum mechanical laws govern this paradigm. We will pay little attention to the physical interpretations of these laws. A mathematical formulation suffices for our purpose.
For defining a quantum mechanical system, we need to enrich our mathematical vocabulary. Let V be a vector space over (or ). Using Dirac’s ket notation we denote a vector ψ in V as |ψ〉.
An inner product (also called a dot product or a scalar product) on V is a function satisfying ...