Qiskit IBM Runtime's sampler, is behaving differently than the Aer Sampler. Where the later is giving correct output.

[sirgeorgesawcon]

Describe the bug : I am working on an Iterative Amplitude Estimation routine that works on sampler. I have a quantum circuit, that I run first using the sampler from aer, I import it from there, simply set
sampler = _Sampler(run_options={"shots": num_shots})

and run the algorithm, It gives me a result of 0.64165 which is very near to what I shoud be getting (i verified it using classical caluclations , it should be around 0.64)

Then I use
from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Estimator, Options

where my qiskit_ibm_runtime version is 0.11.3

Then I run the exact same quantum circuit qc, using backend = "ibmq_qasm_simulator"

options = Options()
options.execution.shots = 2000
options.resilience_level = 0

and then invoke the session and make use of sampler = Sampler(options=options)

The result I'm getting from this is never the same, and is no where close to my answer that I was getting using aer Sampler.

Even though the backend I'm using is IBM_Qasm_simulator , which is error free and ideal simulator, so there should not be any error in the result, but I'm not able to replicate the result that I was getting using the aer sampler. Why is it so? Since both these make use of shot-type backend, the only difference is that one is running on my local device and the other on IBM cloud. But the answers are so different.

Steps to reproduce :
Here's the code for the quantum circuit

n = 3
obj = 8
mu = 4
c = 0.1
sigma = 1
a = 0
b = 7
reps = 2
p_s = 0.5
p_b = 0.2
demand = NormalDistribution(num_qubits=n,mu=mu,sigma=sigma,  bounds=[a,b])
supply = RealAmplitudes(n, reps=reps)
supply = supply.assign_parameters(parameters)
qc = QuantumCircuit(9)
qc.compose(demand,qubits=[3,4,5], inplace=True)
qc.compose(supply, qubits = [0,1,2], inplace=True)
z = 6
z1 = 7
for i in range(n):
    qc.x(i)

for i in range(1,n):
    qc.cnot(z,i)

for i in range(1,n):
    qc.cnot(z,i+n)

qc.ccx(0,n,n+n)

qc.x(0)

for i in range(1,n-1):
  qc.cnot(n+n,i)
  qc.cnot(n+n,i+n)
  qc.ccx(i+n,i,n+n)
  qc.ccx(i+n,i,n)

qc.cnot(n+n,n-1)
qc.cnot(n+n,n+n-1)
qc.ccx(n+n-1,n-1,n+n)

for i in range(1,n-1):
    qc.cnot(n,n-i)
    qc.cnot(n,2*n-i)
    qc.ccx(2*n-i-1,n-i-1,n)

for i in range(1,n-1):
    qc.ccx(0,n,n-i)
    qc.ccx(0,n,2*n-i)

qc.x(0)

qc.ccx(0,n,1)

qc.ccx(0,n,n+1)

for i in range(n):
  qc.x(i)

qc.x(2*n)

for i in range(n):
    qc.x(i+n)

for i in range(1,n):
    qc.cnot(z1,i)

for i in range(1,n):
    qc.cnot(z1,i+n)

qc.ccx(0,n,z1)

qc.x(n)

for i in range(1,n-1):
  qc.cnot(z1,i+n)
  qc.cnot(z1,i)
  qc.ccx(i,i+n,z1)
  qc.ccx(i,i+n,0)

qc.cnot(z1,z1-2)
qc.cnot(z1,n-1)
qc.ccx(z1-2,n-1,z1)

for i in range(1,n-1):
    qc.cnot(0,z1-(i+1))
    qc.cnot(0,n-i)
    qc.ccx(z1-i-2,n-i-1,0)

for i in range(1,n-1):
    qc.ccx(0,n,z1-(i+1))
    qc.ccx(0,n,n-i)

qc.x(n)
qc.ccx(0,n,n+1)
qc.ccx(0,n,1)

for i in range(n):
    qc.x(n+i)
qc.x(z1)

for i in range(n):
    c2ry = RYGate(2*c*p_s * 2**(i)).control(2)
    qc.append(c2ry,[i+n,obj-2,obj])

for i in range(n):
    c2ry = RYGate(2*c*p_s * 2**(i)).control(2)
    qc.append(c2ry,[i,obj-1,obj])

for i in range(n):
    c2ry = RYGate(-2*c*p_s * 2**(i)).control(3)
    qc.append(c2ry,[i,obj-1,obj-2,obj])

for i in range(n):
  qc.cry(-2*c*p_b*(2**i),i,obj)

qc.ry(np.pi/2,obj)
qc.draw('mpl')

Once the quantum circuit qc is made, first we import sampler from :

from qiskit_aer.primitives import Sampler

Then call the IAE function:

epsilon = 0.01   # the error
alpha = 0.5      # the alpha value


problem = EstimationProblem(state_preparation=qc,objective_qubits=[obj])     # the quantum circuit

# construct amplitude estimation
iae = IterativeAmplitudeEstimation(
    epsilon_target=epsilon,
    alpha=alpha,
    sampler=Sampler(run_options={"shots": num_shots})
)

and then:

result = iae.estimate(problem)
print(result)
print((result.estimation-0.5)/c)

The result for the final print command is 0.641

But then, when i make use of :

from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Estimator, Session, Options
# Save an IBM Quantum account.
QiskitRuntimeService.save_account(channel="ibm_quantum", token="MY API TOKEN",overwrite=True)

and then set the backend:

backend = "ibmq_qasm_simulator"

and then the options

options = Options()
options.execution.shots = num_shots
options.resilience_level = 0

and finally calling the IAE:

# runt he circuit on sampler

epsilon = 0.01   # the error
alpha = 0.5



with Session(service=service, backend=backend):
    sampler = Sampler(options = options)
    iae = IterativeAmplitudeEstimation(epsilon_target=epsilon,alpha=alpha, sampler=sampler)
    problem = EstimationProblem(state_preparation=qc,objective_qubits=[obj])
    result = iae.estimate(problem)
    print(result)
    print((result.estimation-0.5)/c)

always give me a different result from what is Intended.

Expected behavior : I expect to see the same behaviour as I was seeing from the aer sampler in qiskit ibm runtime sampler.

Suggested solutions :

Additional Information : I also had a lengthy conversation on Qiskit's slack as well on this said topic
Slack Chat: https://qiskit.slack.com/archives/C7SJ0PJ5A/p1693194989748429?thread_ts=1693194989.748429&cid=C7SJ0PJ5A

• qiskit-ibm-runtime version: 0.11.3
• Python version: 3.10.12
• Operating system: Win

[ElePT]

Hi @sirgeorgesawcon, this bug is most likely in the IterativeAmplitudeEstimation class and not in the Sampler. I would encourage you to:

1. check what is your qiskit-terra version, as a related bug was fixed on the 0.23 release (see Fix the AmplitudeEstimator algorithms for primitive usage qiskit#9394)
2. If the bug persisists, open an issue in https://github.com/qiskit-community/qiskit-algorithms, this is the new location of the qiskit algorithms module. you can check out what this change of location means here: https://qiskit.org/ecosystem/algorithms/release_notes.html#prelude

[sirgeorgesawcon]

Hi The Terra version I'm currently on is 0.25.1 , so yeah, I'll open an issue in qiskit algorithms

[ElePT]

I believe that the core issue is in the qpy module, see Qiskit/qiskit#10735.

[kt474]

Closing this issue for now, can be tracked in the issue linked above