Update dynamics_backend.rst tutorial after next terra release

[DanPuzzuoli]

In the DynamicsBackend tutorial, it was necessary to add the CRPulseGate instruction to the target to make sure the transpiler functions as desired when running the CrossResonanceHamiltonian experiment. This is a work around that shouldn't b necessary.

This behaviour is fixed in Qiskit terra PR 9783, so we should remove this line from the tutorial after the next terra release.

[DanPuzzuoli]

The dynamics_backend.rst tutorial is also now failing to build due to issues with transpilation, so this should be fixed. @wshanks pointed to this PR as introducing the change in the Experiments code that is involved in the error.

[DanPuzzuoli]

Edit: the change described here can be moved to another issue if it makes sense.

In addition to this, a section showing how to get primitives to work with DynamicsBackend should be added to the tutorial. A self contained exampled by @wshanks:

from qiskit_ibm_provider import IBMProvider
from qiskit_dynamics import DynamicsBackend
from qiskit.circuit import ParameterVector, Parameter, QuantumCircuit, Gate
from qiskit.circuit.library import XGate, SXGate, RZGate
from qiskit.primitives import BackendEstimator
from qiskit import pulse
from qiskit.quantum_info import SparsePauliOp
from qiskit.transpiler import InstructionProperties
import numpy as np
​
provider = IBMProvider()
real_backend = provider.get_backend("ibm_perth")
qubit_tgt_register = [0]
dynamics_options = {'seed_simulator': 5000, "configuration": real_backend.configuration()}
dynamics_backend = DynamicsBackend.from_backend(real_backend, subsystem_list=qubit_tgt_register, **dynamics_options)
​
backend = dynamics_backend
​
​
amp_params = np.array([[0.2], [0.22], [0.23]])
batch_size = len(amp_params)
params = ParameterVector("theta", 1)
​
observables = SparsePauliOp.from_list([("X", 1.), ("Y", 1.)])
estimator = BackendEstimator(backend=backend)
​
qc = QuantumCircuit(1)
​
parametrized_circ = QuantumCircuit(1)
​
parametrized_X_gate = Gate("my_x", 1, params=[params[0]])
​
default_schedule = real_backend.instruction_schedule_map.get("x", qubit_tgt_register)
pulse_ref = default_schedule.instructions[0][1].pulse
​
with pulse.build(backend=backend, name="parametrized_schedule") as parametrized_schedule:
    pulse.play(pulse.Drag(duration=pulse_ref.duration, amp = params[0], sigma=pulse_ref.sigma, 
                          beta=pulse_ref.beta, angle=pulse_ref.angle), channel=pulse.DriveChannel(0))
    
with pulse.build(backend=backend, name="sx_schedule") as sx_schedule:
    pulse.play(pulse.Drag(duration=pulse_ref.duration, amp = 0.1, sigma=pulse_ref.sigma, 
                          beta=pulse_ref.beta, angle=pulse_ref.angle), channel=pulse.DriveChannel(0))
​
    
rz_theta = Parameter("theta")
with pulse.build(backend=backend, name="rz") as rz_sched:
    pulse.shift_phase(-rz_theta, channel=pulse.DriveChannel(0))
​
backend.target.add_instruction(XGate(), properties={(0,): InstructionProperties(calibration=sx_schedule)})
backend.target.add_instruction(SXGate(), properties={(0,): InstructionProperties(calibration=sx_schedule)})
backend.target.add_instruction(RZGate(rz_theta), properties={(0,): InstructionProperties(calibration=rz_sched)})
​
parametrized_circ.add_calibration(parametrized_X_gate, qubit_tgt_register, parametrized_schedule)
parametrized_circ.append(parametrized_X_gate, qubit_tgt_register)
​
qc.append(parametrized_circ.to_instruction(), qubit_tgt_register)
​
job = estimator.run(circuits=[parametrized_circ]*batch_size, observables=[observables]*batch_size, parameter_values=amp_params,
                   shots=100)
​
results= job.result().values
print(results)

Everything mentioned here would be a good to include in a 0.4.1 release.