 We briefly discuss the application of vector spaces in quantum physics. Classical information is measured in bits. Implementation of bits in nature involves macroscopic physical systems with at least two different stable states and a low energy reversible transition process (i.e., switches, relays, transistors). The most fundamental way to store information in nature on an atomic level involves qubits. The qubit is described by a state vector in a two-level quantum-mechanical system, which is formally equivalent to a two-dimensional vector space over the complex numbers (Von Neumann 1932; Nielsen &amp; Chuang 2000). Quantum algorithms have, in some cases, a fundamentally lower complexity (e.g., Shor’s algorithm for factorization of integers (Shor 1997)).