I'm an Msc student working on a quantum information project (VQEs on 4 qubits).

Our group is looking at different IBM simulators on the IBM platform, and have noticed that performance is different for simulators such as qasm_simulator and statevector_simulator and aer_simulator_matrix_product_state even without any noise or error modeling.

For example we generated this graph :

enter image description here

Clearly the simulators perform orders of magnitudes differently, but we have no idea why as they should all be ideal simulators for a small qubit system. The descriptions on the IBMQ website don't detail how this is possible.

Is there anywhere we can read about the implementation of these different simulators in detail ?

Any input whatsoever is appreciated, and thanks for reading !

  • $\begingroup$ What exactly are you measuring? My understanding was that the statevector simulator and the qasm simulator are the exact same simulator. The difference is the way the output is returned. $\endgroup$ Commented Dec 20, 2022 at 20:57
  • $\begingroup$ We're measuring the energy of a molecule we defined using a PySCF Driver. We're using the VQE object found in the qiskit.algorithms.minimum_eigensolvers library. $\endgroup$
    – Vinxxc
    Commented Dec 20, 2022 at 22:08
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    $\begingroup$ The statevector simulator will perform exact calculation for the expectation values for the VQE, the other one will be shot-based, I think this is where the difference you see comes fro. And btw the statevector and qasm simulators aren't the same, as I said one will be shot-based (the qasm, approaching best the ideal machine basically), the other one will do exact calculation (all the calculations will use the exact state vectors and operators behind, hence the fact that you have a much "better" energy. MPS is shot-based but represent quantum states differently in the computation. $\endgroup$
    – Lena
    Commented Dec 21, 2022 at 9:19
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    $\begingroup$ The statevector simulator does the linear algebra to get the probabilities as you would do by pen and paper. The qasm silumator on the other hand mimicks the process of obtaining the probability by taking several (finite) measurements and thus has some variance (shot noise). MPS is similar to qasm in this concern, but uses a different method to 'apply the unitaries'. Qasm has a much larger set of native gates. (see quantum-computing.ibm.com/services/programs/docs/runtime/manage/…) $\endgroup$ Commented Dec 21, 2022 at 9:20
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    $\begingroup$ @qcabepislon. I had assumed the qasm simulator still calculates the statevector, and then uses that together with a random number generator to generate the shots. What else can it take probabilities on? The difference is that one returns the large statevector, and the other returns the smaller shots. $\endgroup$ Commented Dec 21, 2022 at 20:17

1 Answer 1


This might help as it gives access to various simulators and quantum hardware for further investigation: "Dear quantum computing students, researchers, and academics. We are excited to announce an offer that will significantly enhance your work in quantum computing and would appreciate your help in spreading the word. Classiq.io/Academia is now available free of charge, providing you with a powerful platform that automates the creation of scalable, optimized quantum circuits and grants access to quantum computers, currently including free computation, thanks to our partnership with Microsoft Azure Quantum."

  • $\begingroup$ Sorry, but I do not see how this is related to the question. The question is about difference in Qiskit simulators and you answered with statement about something new in MS Azure. What about posting at least a link where a better simulator (i.e. what I guess you are trying to tell) can be found. $\endgroup$ Commented Apr 10, 2023 at 21:11
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    $\begingroup$ Thanks for the comment, to clarify, as a student user this would give an access route to other simulators e.g. NVIDIA, IonQ, in a way that you wouldn't have to rework your circuit classiq.io/academia $\endgroup$
    – nomisno
    Commented Apr 13, 2023 at 8:02

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