Title: Quantum Computing: The angle of rotation of the 0 qubelets and 1 qubelets are inconsistent across several pages (pages 400, 402, 406, 407, 413)

Example:

- 0 qubelets are assigned with 20 degrees rotation, 1 qubelets are assigned with -30 degress rotation - (page 400)
- 0 qubelets are assigned with 20 degrees rotation, 1 qubelets are assigned with -30 degrees rotation - (page 402)
- 0 qubelets are assigned with 30 degrees rotation, 1 qubelets are assigned with 20 degrees rotation - (page 406)
- 0 qubelets are assigned with 20 degrees rotation, 1 qubelets are assigned with 30 degrees rotation - (page 407)
- 0 qubelets are assigned with 20 degrees rotation, 1 qubelets are assigned with -30 degrees rotation - (page 413)

Hi,

- Not quite. What’s shown is that starting with qubelets that initially have no orientation, we move the entire qubit (the qubelet orientations are still 0 degrees) through a series of rotations (actually just 2), so that it ends up at any point on the unit sphere we choose. The difference between the 2 rotations we moved the qubit is then shown as the orientation of the triangle |1> qubelets. The latitude on the Bloch sphere tells us the relation between the number of the pentagon |0> qubelets and the triangle |1> qubelets (for example, states near the North Pole have more pentagon |0> qubelets than triangle |1> qubelets). And, the longitude indicates the relative difference in orientations between the pentagon |0> and triangle |1> qubelets. The intent is just to illustrate that any point on the Bloch sphere is equivalently represented as pentagon |0> and triangle |1> qubelets oriented in a mathematically precise way.
- Don’t think of starting with qubelets in a specific orientation.
- The Try Your Hand exercises on Page 156 should shed more light on the relationship between a point on the Bloch sphere (a specific quantum state) and the pentagon |0> and triangle |1> qubelets.
- Not sure if it helps, but think of a solved Rubik’s Cube. When you twist and turn its faces, you are moving the entire face containing the tiny cubies at once. After a few such twists, the tiny cubies end up with different orientations. We are doing something similar here but with with just 2 “faces” each representing the pentagon |0> and triangle |1> qubelets respectively. We rotate the entire face as a unit just as in the Rubik’s Cube. And, the state we end up in is a specific combination of the number of pentagon |0> and triangle |1> qubelets their respective orientations.

Thanks again for your comments. This is a difficult topic and hard to wrap your head around. I find the Bloch sphere highly confusing when designing quantum algorithms.

But, since the qubelets in a qubit are equivalent to quantum states on the Bloch sphere, we can instead use the qubelets model to build quantum circuits that take a qubit from one quantum state. I find this more intuitive than grappling with the Bloch sphere.

Thanks,

Nihal