3
$\begingroup$

Is there a good primer or set of lectures\examples that show entirely how to take a given matrix and developing a circuit that represents it. I am trying to implement a program to find the lowest Eigenvalue - VQE approach - using quantum circuits. So far, what I have done, using tutorials I found, is as follows:

$H_{total} = H_1(\theta_1) + H_2(\theta_2) + H_3(\theta_3)$

I have been relying on simulating each term of the hamiltonian, the $H_i$, as separate circuits and measuring the expected values as $\theta_i$ changes.

However, as I have been told by my TA that one cannot simulate the hamiltonians separately to find the ground state.

$\endgroup$
11
  • $\begingroup$ Hi Enrique. How I understand VQE one doesn't need to evaluate the Hamiltonian H. One needs to represent H as a sum of Pauli terms and try to find the expectation values of each Pauli term without evaluation. Here is a link to my tutorial for VQE, where I didn't evaluate the Hamiltonian or a part of it. github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/… $\endgroup$ Feb 22 '20 at 7:55
  • 1
    $\begingroup$ Hi, I actually followed your tutorials ! Thanks for the feedback! $\endgroup$ Feb 22 '20 at 8:10
  • $\begingroup$ I am actually a bit confused. I am wondering how I can in one circuit have the hamiltonian rather than what I am currently doing: creating two circuits, one representing XX + YY since they commute, and another representing ZZ? $\endgroup$ Feb 22 '20 at 8:11
  • $\begingroup$ One question do you want to find minimal eigenvalue of your presented $H_{total}$? If yes then why you are changing it with $\theta$s? I think $H_{total}$, in that case, shouldn't be changed $\endgroup$ Feb 22 '20 at 8:31
  • $\begingroup$ In VQE we are changing the prepared state. And we don't evaluate $XX$ or $YY$, we just measure the $\left\langle \psi \right| XX \left| \psi \right\rangle$, where $\psi$ is our prepared state. How calculate the $\left\langle \psi \right| XX \left| \psi \right\rangle$? We just simply measure what is the probability of measuring eigenvectors of $XX$ that have +1 eigenvalue ($\left| ++ \right\rangle$, $\left| -- \right\rangle$) and substarcting the probability of measuring eigenvectors of $XX$ that have -1 eigenvalue ($\left| +- \right\rangle$, $\left| -+ \right\rangle$). $\endgroup$ Feb 22 '20 at 8:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.