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Is there a way to get certain measurement results by variational quantum eigensolver in qiskit? More specifically, I want to get measurement results for certain operators, like $\langle a^\dagger_ia_j\rangle$ (which I assume that I later transform it into the qubit version using Jordan-Wigner transformation) for every $i,j$ in the system. Therefore, I need to get the measurement results for the matrix for, say, $10^4$ shots. I noticed that the VQE class provides the function to calculate the expection value, can I use this function to get my job done, or there are any other ways to achieve this?

ironmanaudi
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    Do you have the state with respect to which you want to compute the expectation value available, or do you need to prepare it first with the VQE? If you have it available, you can use Qiskit's operators directly. Otherwise, if you first need to optimize your state with the VQE, you can pass aux_operators to VQE.compute_minimum_eigenvalue to evaluate the observable at the final state. – Cryoris Apr 11 '21 at 12:42

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$\newcommand{\Ket}[1]{\left|#1\right>}$ $\newcommand{\ket}[1]{|#1\rangle}$ $\newcommand{\bra}[1]{\left<#1\right|}$

I think you can find the answer to your question here: Circuit for VQE Expectation Value Finding

If you want to get the expectation value (average value) of an operator corresponding to an observable on a quantum state you can follow this formula:

$E(M) = \braψM\ketψ $

Here an example code:

from qiskit import QuantumCircuit
import numpy as np
from qiskit.aqua.operators import StateFn
from qiskit.aqua.operators import Z

qc = QuantumCircuit(2)
qc.rz(np.pi/3, [0])
qc.rx(np.pi/3, [0])
qc.cx(0, 1)


operator = Z
psi = StateFn(qc)
expectation_value = (~psi @ operator @ psi).eval()
print(expectation_value.real)
BẢO BẠCH GIA
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  • Is this calculation or measurement of the code given? I need to run the circuit on a real quantum device, so I need to measure the expectation value of the obeservable which contains a lot of anti-commute term. – ironmanaudi Apr 13 '21 at 06:52
  • Moreover, Can I input a matrix or tensor (each term is a Pauli string) to the expectation function? – ironmanaudi Apr 13 '21 at 07:21
  • The code above is the calculation of expectation value. If you want to measure the expectation value you should check this link: https://qiskit.org/documentation/apidoc/qiskit.aqua.operators.expectations.html – BẢO BẠCH GIA Apr 13 '21 at 09:27
  • You can input a matrix and tensor to the expectation function as well – BẢO BẠCH GIA Apr 13 '21 at 09:28
  • Thanks. Is there any requirements for the tensor (in my case, it is a four-index tensor), like the data structure? In my case, each element of the tensor is a Pauli string, and should I claim the whole tensor as something in qiksit? – ironmanaudi Apr 13 '21 at 12:22
  • I think there are no requirements for your tensor and yeah you should claim the tensor as a matrix and put in into qiskit – BẢO BẠCH GIA Apr 13 '21 at 12:56
  • So, in this case, I can input a 3-index tensor like this [[[a,b,c], [d,e,f]], [[c,e,f],[l,m,d]]] with its data structure as python list and elements as Pauli strings, is that right? – ironmanaudi Apr 13 '21 at 13:02
  • Yeah I think you can but you should use NumPy to create that matrix . – BẢO BẠCH GIA Apr 16 '21 at 10:36