Difference between IBM simulator backends

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 :

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 !

• 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. Dec 20, 2022 at 20:57
• 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. Dec 20, 2022 at 22:08
• 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.
– Lena
Dec 21, 2022 at 9:19
• 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/…) Dec 21, 2022 at 9:20
• @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. Dec 21, 2022 at 20:17