Lecture 15 - Implementations of Quantum Computing (cont)

See:

![[Physics CPE 345 Quantum Computing Lecture slides Week 6 Implementation of quantum computing 240506.pdf#page=6]]

Example

The 87 Rb isotope has a nuclear spin quantum number of $I = 3 / 2$ . Rb is an alkali (first group in the periodic system) which implies that is has all full shells plus one electron in the outermost shell. This results in its spin quantum number being $S = 1 / 2$ .

Find the total angular momentum quantum number $F$ for the lowest six states of the hyperfine energy level diagram of 87 Rb.

We are on the outermost shell, so we have some [Element] $n s^{1}$ orbital. That means that $l = 0$ so then:

j = | 0 - \frac{1}{2} |, . . ., \frac{1}{2} = {0.5}

And:

F \in {1, 2}

We can generalize with changing $l = 0, . . ., 5$ :

$l$	Range of $j$	Range of $F$
0	0.5	1, 2 (only from 0.5 case)
1	0.5, 1.5	0, 1, 2, 3 (mainly from 1.5 case)
Notice in the diagram on:

![[Physics CPE 345 Quantum Computing Lecture slides Week 6 Implementation of quantum computing 240506.pdf#page=7]]

We have:

5^{2} S_{1 / 2}

Is of the form:

n^{2s+1}l_j $$So for $5^{2}S_{1/2}$ we have $l = 0$ from the $S$ and we have $j = 1/2$ range as a result. We didn't draw $5^2P_{1/2}$ because it's **in-between** the other two states in the diagram. ### How it Works? There are some common decoherence mehanisms: - Accidental absorption of photons from light pattern holding the atoms/qubits - Energy from moving traps around to shuttle atoms/qubits or move them closer for 2-qubit gates. We will use (focused) laser beams to initialize, rotate, and read out single qubit gate. ![[Physics CPE 345 Quantum Computing Lecture slides Week 6 Implementation of quantum computing 240506.pdf#page=12]] If we want to go from $F = 2$ to the upper state $F' = 1$ then it can fall down to *either* $F=1$ OR $F = 2$ since an arbitrary proton moves any state from the $F'$'s up/down/neither 1 level at max.