Quantum logic
Quantum systems evolve according to ?new = U?old
- U = eiHt is a unitary operator derived from the Hamiltonian H
- H is a unitary matrix that represents the total energy of the system
Unitary transformations
- Every quantum state is a vector of unit length
- The probabilities must sum to one
- Quantum gates map unit vectors to unit vectors
- Mappings with this property are called unitary transformations
To make a quantum computer out of qbits, we design an H so that U acts like a logic gate
- Quantum computers are deterministic, linear, and unitary