How to use local transpilation with ibmq primitives?

Question

I want to use IBMQ's runtime Estimator primitive to address their systems. Since it has no function to return the transpiled circuit, but I need the knowledge what circuit exactly was executed in the end, I want to do the transpilation locally and then give that circuit into the estimator.

For the transpiling I add the needed post-rotations for measuring non-PauliZ, then add the classical registers for the measurements and then transpile this circuit. So I end up with a complete circuit with classical registers and qubits on which nothing happens, they are just part of the device. (see code below)

What is a elegant way to separate this into a circuit and an observable that I can pass to the estimator?

minimal `code example:

from qiskit import QuantumCircuit, transpile, IBMQ
from qiskit_ibm_runtime import QiskitRuntimeService
backend='ibmq_quito'
service=QiskitRuntimeService()
backend=service.get_backend(backend)

#circuit
circuit = QuantumCircuit(2)
circuit.h(0)
circuit.cx(0, 1)

#post-rotations: want to measure 'XZ'
meas_circuit= QuantumCircuit(2)
meas_circuit.h(0)

#add post-rotations to circuit
full_circ=circuit.compose(meas_circuit).measure_all(inplace=False)

#transpile
trans_circ = transpile(full_circ, backend)

print(trans_circ)

I want to use the estimator to measure the expectation value of ZZ on the non-idle qubits of trans_circ.

Since I need the same number of observables and qubits, can I just take the identity as observable for the qubits I am not interested in? Those will just give factors of 1 to each term of the expectation value. What I tried was:

service=QiskitRuntimeService()
session=Session(service=service, backend=backend)
options=Options()
options.resilience_level=3
estimator=Estimator(session=session, options=options)

params=[]
obs=SparsePauliOp.from_list([("IIIZZ", 1)])


job=estimator.run(circuits=trans_circ, observables=obs, parameter_values=params)
expvals=job.result().values
print(expvals)

This gives me some output, but I am not sure whether it is correct: It returns values around 0.95 while I calculated an expectation value of 0.5 on paper. Is there a mistake or do I see the impact of noise of the hardware here like in this question?

Also what happens to the measurement instructions here? Are they ignored? Do I need them or better separate?

Answer 1

The problem here should be in how your are creating your SparsePauliOp observable: if you want to measure the expectation value of $Z_0Z_1$ (non-idle qubits of the transpiled circuit), you have to do

obs = SparsePauliOp.from_list([("IIIZZ", 1)])

and not

obs = SparsePauliOp.from_list([("ZZIII", 1)])

Take a look to the qiskit.quantum_info.SparsePauliOp.from_list documentation for more details.