Bonaparte Quantum Algebra

Vectors

Below are the core mathematical ingredients of quantum computation, quantum vectors that define how states are represented and linear transformations that show how those states evolve.

Quantum Vectors:
  • State Representation: A quantum vector |ψ⟩ represents the state of a system in multidimensional space.
  • Superposition: |ψ⟩ = [α β]^T captures all possible superpositions of basis states |0⟩ and |1⟩.
  • Computational Basis: The fundamental states that form the building blocks of quantum computation.
Linear Transformations:
  1. Matrix Operations: Linear transformations represented by matrices act on vectors to produce new states.
  2. Quantum Gates: Unitary operators that preserve probability and phase in quantum systems.