Different results with the same circuit depending on whether executed on a simulator or on a real backend. Could you help me in understanding why?

Question

The same 4 qubits circuit yields different results whether it runs on a simulator or on a real system and I would appreciate if you could help me in understanding the reason of this difference or point me in the right direction.

The purpose of the experiment is to eliminate (almost) all probabilities for measuring state |0000> (or more exactly state |000> as qbit 3 has an ancilliary role). I observe that this works on a simulator (even though I haven't yet suceeded in reshufling probabilities evenly) but state |0000> is still alive an well with the real backend.

Below are the two extract of the code differing only by the instructions relative to the backend. The attached picture show the output of both cases.

In the two documented cases the backend is Ibmq_Bogota, Qiskit version 1.6.20

Extract 1.1 : simulator

simulator = Aer.get_backend('aer_simulator')

#Circuit definition
qcMq = QuantumRegister(3,'qcMq')
qcMa = QuantumRegister(1,'qcMa')
qcMc = ClassicalRegister(4, 'qcMc')
qcM = QuantumCircuit(qcMq, qcMa, qcMc)

#Init
qcM.reset(qcMq)
qcM.reset(qcMa)
qcM.x(0)
qcM.h(0)
qcM.h(1)
qcM.h(2)
#qcM.h(1)

qcM.x(1)
qcM.x(2)
#qcM.h(2)

#swap test
qcM.h(qcMa[0])
qcM.cswap(qcMa[0], qcMq[1], qcMq[2],ctrl_state='1')
qcM.h(qcMa[0])
qcM.x(qcMa[0])
qcM.barrier()

#H on qubit 0 if all other qubits in state |1>
qcMz = MCMT('h', num_ctrl_qubits=3, num_target_qubits=1) #ok
qcMf = qcM.compose(qcMz,qubits=[3,2,1,0])
qcMf.barrier()

qcMf.x(1)
qcMf.x(2)
qcMf.barrier()

# Hadamard on qbit 1 et 2 if result swap test = 1 and qbubit 0 = 1
qcMy = MCMT('h', num_ctrl_qubits=2, num_target_qubits=2) #ok
qcMr = qcMf.compose(qcMy,qubits=[3,0,1,2]) #ok 
qcMr.barrier()

#qcMr.cx(2,1)

#Statevector du circuit décrit =============
st1 = Statevector.from_instruction(qcMr)
D=st1.draw(output='bloch')
show_figure(D)
print('')
print(st1)

D=plot_state_qsphere(st1)
show_figure(D)
#==========================
qcMr.reset(3)
#measure 
qcMr.measure([0,1,2],[0,1,2])

#Print circuit ; print(qcM) also works
qcMP = qcMr.draw(output='mpl')  
show_figure(qcMP)

#If simulator 
simulator = Aer.get_backend('aer_simulator')
qcMr = transpile(qcMr, simulator)
``` end of extract 1.1
Extract 1.2 - simulator 

# if simulator
result = simulator.run(qcMr, memory = True).result()
counts = result.get_counts(qcMf)
mem=result.get_memory()
plot_histogram(counts, title='test')

``` Extract 2.2 - real backend 
#Circuit definition
qcMq = QuantumRegister(3,'qcMq')
qcMa = QuantumRegister(1,'qcMa')
qcMc = ClassicalRegister(4, 'qcMc')
qcM = QuantumCircuit(qcMq, qcMa, qcMc)

#Init
qcM.reset(qcMq)
qcM.reset(qcMa)
qcM.x(0)
qcM.h(0)
qcM.h(1)
qcM.h(2)
#qcM.h(1)

qcM.x(1)
qcM.x(2)
#qcM.h(2)

#swap test
qcM.h(qcMa[0])
qcM.cswap(qcMa[0], qcMq[1], qcMq[2],ctrl_state='1')
qcM.h(qcMa[0])
qcM.x(qcMa[0])
qcM.barrier()

#H on qubit 0 if all other qubits in state |1>
qcMz = MCMT('h', num_ctrl_qubits=3, num_target_qubits=1) #ok
qcMf = qcM.compose(qcMz,qubits=[3,2,1,0])
qcMf.barrier()

qcMf.x(1)
qcMf.x(2)
qcMf.barrier()

##Hadamard on qhbit 1 et 2 if result swap test = 1 and qbubit 0 = 1
qcMy = MCMT('h', num_ctrl_qubits=2, num_target_qubits=2) #ok
qcMr = qcMf.compose(qcMy,qubits=[3,0,1,2]) #ok 
qcMr.barrier()

#qcMr.cx(2,1)

#Statevector from the declared circuit 
st1 = Statevector.from_instruction(qcMr)
D=st1.draw(output='bloch')
show_figure(D)
print('')
print(st1)

D=plot_state_qsphere(st1)
show_figure(D)
#=== 
qcMr.reset(3)
#mesure 
qcMr.measure([0,1,2],[0,1,2])
``` End of extract 2.1 - real backend 

``` Extract 2.2 - real backend 
 
    #If real system *******
    job_exp = execute(qcMr, backend, shots=nbshots, max_credits=max_credits, memory=True)
    job_monitor(job_exp)
    result = job_exp.result()
    counts = result.get_counts()
    mem = result.get_memory()
``` End of extract 2.2 - real backend 
END OF QUESTION


  [1]: https://i.stack.imgur.com/FaE2X.png

Answer 1

The issue is probably that your circuit is so large that you're being overwhelmed by noise on the real system. You're doing dozens of two qubit gates (it's hard to give an exact number since you're relying on whatever automatic decomposition is happening behind the scenes), and each has error rates around 1-2%...

It's also noteworthy that it looks like the outputs that decreased have more 1s than 0s, which is consistent with decay to the ground state being an issue.

You should try running something smaller and simpler, then slowly build up.

Answer 2

Indeed, what you’re seeing here is amplitude damping (T1 decay) which is a major source of error, and is biased towards the ground state. I’m not sure what’s the noise model in the Aer simulator, but if it’s a depolarizing channel or other Pauli-error based simulator, it won’t show this effect, since Pauli errors are not conditioned on the state whereas amplitude damping is.

As Craig Gidney suggested once, you can negate the effect of amplitude damping to some extent by adding X gates in various locations, but you need make sure that you take their effect into account by commuting them out of the circuit.