# How do I find the qubit trajectory on the Bloch sphere when implementing an RY rotation on an IBM backend?

Suppose I use Qiskit to prepare the $$| + \rangle$$ state using a RY rotation,

import numpy as np
from qiskit import QuantumCircuit

circ = QuantumCircuit(1)
circ.ry(np.pi / 2, 0)


I would like to know the Bloch sphere trajectory of the qubit on the physical level when I do this. Naively, I would expect that this is implemented as a rotation $$\pi / 2$$ rotation about the $$Y$$ axis which is the minimal distance path. But as I know, this circuit can be introspected in various ways.

For example, when I transpile the ciruit to the ibmq_armonk backend, I get the following circuit level description

which suggests that actually the qubit goes from $$| 0 \rangle$$ to the xy-plane at some angle $$\pi / 4$$ away from $$+x$$ and is then corrected with the final $$RZ(\pi / 2)$$.

I can then introspect even further at the pulse-level using the build_schedule utility obtained via from qiskit import schedule as build_schedule to obtain the description of the circuit as

Schedule((0, ShiftPhase(-1.5707963267948966, DriveChannel(0))), (0, Play(Drag(duration=320, amp=(0.3705139948561776-0.07637772314715083j), sigma=80, beta=-1.0562934233232557), DriveChannel(0))), (320, ShiftPhase(-4.71238898038469, DriveChannel(0))), name="circuit32")


Is there a way--from the pulse level description--to infer the time-dynamics of the state as I apply the RY rotation? It seems like I could possibly apply the DRAG pulse with half the amplitude, but

1. I'm not sure how to simulate pulse schedules to get the output state
2. I'm not sure that is sound since the DRAG pulse has a complicated definition.

In regards to (1), I tried the following code

backend_sim = qiskit.providers.aer.PulseSimulator()
backend_sim.set_options(system_model=backend.backend)
pulse_qobj = assemble(sched.sched, backend=backend_sim)
results = backend_sim.run(pulse_qobj)


by attempting to guess what system_model meant in this guide, but this didn't work. Note that backend.backend is just the armonk backend wrapped into a custom class and sched.sched is just a Schedule object with the DRAG pulse and measurement also wrapped into a custom class.