# What causes the random variations in the probabilities with respect to the theoretical values, in IBM and QASM simulators?

When I measure 2 and 3 qubits after putting H gate on all of them, there is a variation in probabilities of results in comparison with theoretical values (25% and 12.5%, respectively).

This occurs on different IBM machines and QASM simulators. What causes these differences?

• I take it you're applying the Hadamard gate to all n qubits and then measuring them, expecting to get an equal superposition of all n qubit states... The real backends and the QASM Simulator are all noisy, which means you will see small deviations from the expected values of 25% (for n=2 qubits) or 12.5% (for n=3 qubits). – Aditya Giridharan Sep 12 at 3:07
• @AdityaGiridharan: Just to note that simulator is not noisy. Variances in results are caused by sampling errors. However, you can set the simulator to simulate also noise but default setting is without noise. – Martin Vesely Sep 13 at 6:04
• @MartinVesely I see, thanks for the information! – Aditya Giridharan Sep 13 at 9:43