Qiskit: set_frequency workaround in PulseSimulator

Question

I am trying to run exercise 4 from the recent IBM Quantum Challenge using a PulseSimulator since the device used in the challenge is not available for public use. A snippet of what I am trying to run is the following:

from qiskit import pulse, IBMQ, assemble
from qiskit.pulse import Play, Schedule, DriveChannel, Gaussian, AcquireChannel
from qiskit.providers.aer import PulseSimulator
from qiskit.tools.monitor import job_monitor
import numpy as np

# Constants and units

job_params = {
    'meas_level': 1,
    'meas_return': 'avg',
    'shots': 512
}

spec_range = 0.300 # GHz
num_spec01_freqs = 71
GHz = 1.0e9 # Gigahertz

# Helper functions

def get_exc_chans(gv):
    return [AcquireChannel(i) for i in range(gv['backend_config'].n_qubits)]

def get_spec01_freqs(center_freqs, qubit):
    center_freq = round(center_freqs[qubit], -8) # 2 significant digits
    return np.linspace(center_freq/GHz - spec_range/2,
        center_freq/GHz + spec_range/2, num_spec01_freqs)

# Set up backend and config

provider = IBMQ.load_account()
backend_name = 'ibmq_armonk'
backend_real = provider.get_backend(backend_name)
backend = PulseSimulator.from_backend(backend_real)

qubit = 0

backend_config = backend.configuration()
exc_chans = get_exc_chans(globals())
dt = backend_config.dt

backend_defaults = backend.defaults()
center_frequency = backend_defaults.qubit_freq_est
inst_sched_map = backend_defaults.instruction_schedule_map 

# |0⟩ -> |1⟩  pulse

# Retrieve calibrated measurement pulse from backend
meas = inst_sched_map.get('measure', qubits=[qubit])

# The same spec pulse for both 01 and 12 spec
drive_amp = 0.25
drive_duration = inst_sched_map.get('x', qubits=[qubit]).duration

# Calibrated backend pulse use advanced DRAG pulse to reduce leakage to the |2> state.
# Here we will use simple Gaussian pulse
drive_sigma = drive_duration // 4 # DRAG pulses typically 4*sigma long. 
spec_pulse = Gaussian(duration=drive_duration, amp=drive_amp, 
                        sigma=drive_sigma, name=f"Spec drive amplitude = {drive_amp}")

# Construct an np array of the frequencies for our experiment
spec_freqs_GHz = get_spec01_freqs(center_frequency, qubit)

# Create the base schedule
# Start with drive pulse acting on the drive channel
spec01_scheds = []
for freq in spec_freqs_GHz:
    with pulse.build(name="Spec Pulse at %.3f GHz" % freq) as spec01_sched:
        with pulse.align_sequential():
            # Pay close attention to this part to solve the problem at the end
            pulse.set_frequency(freq*GHz, DriveChannel(qubit))
            pulse.play(spec_pulse, DriveChannel(qubit))
            pulse.call(meas)
            
    spec01_scheds.append(spec01_sched)

qobj = assemble(spec01_scheds, backend=backend, **job_params)
spec01_job = backend.run(qobj)
job_monitor(spec01_job)

However, everytime I run this I get the following (not very helpful) error message:

Job Status: job incurred error

I opened an issue about this in the Qiskit Aer GitHub repository (issue #1264) and got a response. They told me that "the set/shift frequency instructions are not supported by the pulse simulator". And they suggested the following workaround:

A way to bypass this issue as a user is to manually add an oscillation to the pulse envelopes. E.g. if the channel's LO frequency is $w$, but you want to set it to $v$ for a given pulse (or pulses), convert the pulse to an explicit WaveForm specified in terms of a sample list, then multiply the sample array $exp(i(v-w)t)$, where $t$ is the array of associated times. I may be missing some book keeping here but some version of this should work.

As simple as this sounds, I don't quite understand how to do this. Can anyone explain to me, with code, how to do this? Or point me to somewhere where this is done?

Answer 1

So, if you just want to create Pulse to go from ground state $|0\rangle$ to first excited state $|1\rangle$ for can do it with simulator by using a fake Armonk and following the tutorial : https://qiskit.org/textbook/ch-quantum-hardware/calibrating-qubits-pulse.html and https://qiskit.org/textbook/ch-quantum-hardware/accessing_higher_energy_states.html

but if you want to get the 2nd energy state $|2\rangle$ with a simulator you need to construct your own oscillator by using the dim_oscillator, the oscillator allow you to create noise in your system. The lib doc : https://qiskit.org/documentation/stubs/qiskit.providers.aer.pulse.duffing_system_model.html and here the textbook entry : https://qiskit.org/textbook/ch-quantum-hardware/hamiltonian-tomography.html

The think to know is the $|2\rangle$ is a singular property of transmon qubit and so can't be simulate with perfect qubit in other way than having noise or a physical like system.

Here some other tutorial explaining how to do get energies states from custom model https://qiskit.org/documentation/tutorials/circuits_advanced/10_pulse_simulator_backend_model.html?highlight=oscillator and https://qiskit.org/documentation/tutorials/circuits_advanced/09_pulse_simulator_duffing_model.html

I'm absolutly not an expert at all so maybe this way isn't the best way to get to do it.

As simple as this sounds, I don't quite understand how to do this.

Oh and yes I didn't find it easy at all neither