Overview

Last class:

• Quantum computing
• Quantum weirdness
• QM Laws 1, 2, 3

Today:

• A qubit is already very powerful for computation
• EV bomb
• Multiqubit systems

Quantum Laws

Law 1: If a system can be in one of two options, its state is described by $\alpha|0\rangle + \beta|1\rangle$.

Law 2: If you can measure some $|\psi\rangle$ in an “HV” device, it is $|0\rangle$ with prob $\alpha^2$ and $|1\rangle$ with $\beta^2$.

Law 3a/3b: We can build devices to rotate/reflect states

Law 3c: For any two perpendicular vectors $|u\rangle$ and $|v\rangle$ we can build a “UV” device such that for some $|\psi\rangle$ such that it is $|u\rangle$ with probability $\mathrm{proj}_{|u\rangle} |\psi\rangle$ (and similiar for $|v\rangle$).

Example: Horizontal Polarizing Filter

1. Measures photon using “HV” devices
2. If the outcome is $|0\rangle$, then it goes through
3. If the outcome is $|1\rangle$, then it is absorbed and it gives out heat.

Interestingly, if we put in random light into this polarizer, it will output horizontal light at half intensity.