Bloch Rotation matrix discrepancy

Questions
1

I created a Bloch rotation matrix in two different ways that should be equivalent, but they produce slightly different answers. I would like to know if there is a bug OR (more likely) something I don’t understand. Please see attached notebook for a simple example.

Open in Wolfram Cloud ↗

Bloch Rotation Anomaly.nb (15.8 KB)

2

I don’t think you can reconstruct this rotation matrix from RX, RY, and RZ because Pauli matrices do not commute. This should correspond to the bRotate1:

bRotate3[\[Theta]_, n_] := 
 Normal@Exp[
    Total@MapThread[-I #2 \[Theta]/2 QuantumOperator[#1] &, {{"X", 
        "Y", "Z"}, n}]]["Matrix"]
3

Nikolay: Thanks, your suggestion indeed worked. And I found two other forms that work as well in the meantime..