20、The Imminent Arrival of Universal Quantum Computing

The Imminent Arrival of Universal Quantum Computing

1. Unitary Transformations in Quantum Systems

In quantum systems, assuming we can control the Hamiltonian, the state can be rotated by a specific angle. For a spin - 1/2 system, a unitary transform takes the form (\hat{U}=\cos(\theta/2)I - i\sin(\theta/2)\hat{n}\cdot\hat{\sigma}). It’s important to note that any product of unitary operators is also unitary, as shown by ((\hat{U}\hat{V})(\hat{U}\hat{V})^{\dagger}=\hat{V}^{\dagger}\hat{U}^{\dagger}\hat{U}\hat{V}=\hat{I}).

The Copenhagen Interpretation restricts time evolution to unitary operators, which implies that certain types of evolution, like quantum no - cloning and non - erasure, are considered impossible. However, this is only up to the ‘semi -