# How to compare the output of statevector_simulator and qasm_simulator in Qiskit

I am stuck with a very difficult problem. Suppose, I execute a circuit on statevector_simulator, and I get all the values negative. Suppose, now i execute the same circuit on qasm_simulator. I will surely get positive coefficients, because here I will do the square root of the probabilities and probabilities are always positive. Now how should I check the equivalence or correctness?

Edit To make my question more clear, am running a small two qubit circuit using qasm simulator and statevector simulator. You will see that results are different and I am not sure how to compare their results.

Qasm_Simulator

 from qiskit import QuantumCircuit, execute
from qiskit import IBMQ
from qiskit import Aer

import numpy as np
import matplotlib.pyplot as plt

simulator_used = 'qasm_simulator'

circuit = QuantumCircuit(2,2)
data = np.array([-0.5, -0.2, -0.2, -0.6])
norm_data = np.linalg.norm(data)
normalized_data = data/ norm_data
circuit.initialize(normalized_data, [0,1])
circuit.h(0)

circuit.cx(0,1)
circuit.x(0)
circuit.rx(-np.pi/10, 0)
circuit.ry(-np.pi/20, 1)

circuit.measure([0,1],[0,1])

print(circuit)

simulator = Aer.get_backend(simulator_used)

job = execute(circuit, simulator, shots=10000)

result = job.result()

counts = result.get_counts(circuit)

final_result = []

for key in counts:
final_result.append(np.sqrt(counts[key]/10000))

print(final_result)


The result is:

  IBMQ.load_account()
┌──────────────────────────────────────────────────┐┌───┐         ┌───┐    ┌───────────┐┌─┐
q_0: ┤0                                                 ├┤ H ├──■──────┤ X ├────┤ Rx(-π/10) ├┤M├
│  Initialize(-0.60193,-0.24077,-0.24077,-0.72232) │└───┘┌─┴─┐┌───┴───┴───┐└────┬─┬────┘└╥┘
q_1: ┤1                                                 ├─────┤ X ├┤ Ry(-π/20) ├─────┤M├──────╫─
└──────────────────────────────────────────────────┘     └───┘└───────────┘     └╥┘      ║
c: 2/═════════════════════════════════════════════════════════════════════════════════╩═══════╩═
1       0
[0.6433506042586733, 0.6260990336999411, 0.30016662039607267, 0.322490309931942]


Statevector_Simulator

from qiskit import QuantumCircuit
from qiskit.compiler import transpile
from qiskit import IBMQ
from qiskit import Aer

import numpy as np

import matplotlib.pyplot as plt

simulator_used = "statevector_simulator"
circuit = QuantumCircuit(2,2)
data = np.array([-0.5, -0.2, -0.2, -0.6])
norm_data = np.linalg.norm(data)
normalized_data = data/ norm_data

circuit.initialize(normalized_data, [0,1])

circuit.h(0)

circuit.cx(0,1)
circuit.x(0)

circuit.rx(-np.pi/10, 0)
circuit.ry(-np.pi/20, 1)
print(circuit)

simulator = Aer.get_backend(simulator_used)

result = simulator.run(transpile(circuit, simulator)).result()

output_complex = result.get_statevector(circuit)
output_real = np.array(np.real(output_complex))

print("The output real =", output_real)


The result is:

IBMQ.load_account()
┌──────────────────────────────────────────────────┐┌───┐         ┌───┐    ┌───────────┐
q_0: ┤0                                                 ├┤ H ├──■──────┤ X ├────┤ Rx(-π/10) ├
│  Initialize(-0.60193,-0.24077,-0.24077,-0.72232) │└───┘┌─┴─┐┌───┴───┴───┐└───────────┘
q_1: ┤1                                                 ├─────┤ X ├┤ Ry(-π/20) ├─────────────
└──────────────────────────────────────────────────┘     └───┘└───────────┘
c: 2/════════════════════════════════════════════════════════════════════════════════════════

The output real = [ 0.31548377 -0.63950225 -0.27784191 -0.62437088]


It would be great if someone can help me in resolving my problem.

• Please provide a sample output from these two simulations. Feb 11 at 2:02
• I have edited the question @NickMertes.
– Manu
Feb 16 at 15:45

output_real = np.array(np.real(output_complex))


You should not be looking at output_real. In order to compare the results of these two simulations, you should instead be looking at the norm of the complex entries of output_complex. You will see that these norms are very close to the values in final_result (the values won't be exactly equal because of randomness in the simulation).

Also be careful about the order of the entries in final_result. They should be ordered according to '00', '01', '10', '11', but counts is not always returned in that order.

Here is a slim version of your code which gives the expected result

from qiskit import QuantumCircuit, execute
from qiskit import Aer
from numpy import pi, array, sqrt
from numpy.linalg import norm

data = array([-0.5, -0.2, -0.2, -0.6])
norm_data = norm(data)
normalized_data = data / norm_data

qasm_sim = Aer.get_backend('qasm_simulator')
statevector_sim = Aer.get_backend('statevector_simulator')

def create_qc():
qc = QuantumCircuit(2)
qc.initialize(normalized_data, [0,1])
qc.h(0)
qc.cx(0,1)
qc.x(0)
qc.rx(-pi/10, 0)
qc.ry(-pi/20, 1)
return qc

# qasm simulator
qc = create_qc()
qc.measure_all()

result = execute(qc, qasm_sim, shots=10000).result()
counts = result.get_counts()

print('qasm simulator:',
[
sqrt(counts['00'] / 10000),
sqrt(counts['01'] / 10000),
sqrt(counts['10'] / 10000),
sqrt(counts['11'] / 10000)
]
)

# statevector simulator
qc = create_qc()

result = execute(qc, statevector_sim).result()
v = result.get_statevector()

print('statevector simulator',
[
norm(v[0]),
norm(v[1]),
norm(v[2]),
norm(v[3])
]
)


A sample output is

qasm simulator: [0.3377869150810907, 0.6431174076325411, 0.29274562336608895, 0.6217716622683925]
statevector simulator [0.33134439021006384, 0.6414514034928228, 0.29491606277662025, 0.6259197296377109]

• Thank you @Nick Mertes for great help.
– Manu
Feb 22 at 20:11

In the first case, you are simulating classically the behavior of the quantum state entering the circuit at each step. The cost of such a process will become exponential as the size of the state increases.

In the second case, you're imagining you have a quantum computer and you readout the output of the state measurements. Thus you can approximate the probabilities. Except in specific case, you should not assume that the state amplitudes will be the square-root of the probabilities.

Now if you are interested in getting the amplitudes, you should perform another procedure which is going to be more costly. You can look for Quantum Phase Estimation or this topic which explain how to discriminate amplitude signs Is there a way to know if a probability amplitude is negative or positive?

Also the qasm simulator as an option to use the statevector method.

• Thank you @baptistechev. I will go through the concept provided by you.
– Manu
Feb 22 at 20:13