I would like to convert my qubit hamiltonian fom the HeH+ system that I have obtained using Qiskit to an Ising or QUBO model. I have seen multiples examples from QUBO to Qubit Hamiltonian but on the other direction no. Does anyone know how I can do it? Attached my Qubit Hamiltonian. Qubit Hamiltonian


1 Answer 1


One way to do it would be to use a transformation, such as this one:

\begin{align} X_i &= \frac{1 - Z_{i,j}Z_{i,k}}{2}\textrm{sgn}(j)\textrm{sgn}(k)\tag{1}\\ Y_i &= \textrm{i}\frac{Z_{i,k}-Z_{i,j}}{2}\textrm{sgn}(j)\textrm{sgn}(k)\tag{2}\\ Z_i &= \frac{Z_{i,j}+Z_{i,k}}{2}\textrm{sgn}(j)\textrm{sgn}(k)\tag{3}\\ I_i &= \frac{1 + Z_{i,j}Z_{i,k}}{2}\textrm{sgn}(j)\textrm{sgn}(k)\tag{4}.\\ \end{align}

Then all of your $X$ and $Y$ operators will be $Z$ operators. In other words, you've transformed a general XYZ model into an Ising model with the help of auxiliary qubits with labels such as $(i,j)$ and $(i,k)$.

  • 1
    $\begingroup$ First of all thank you very much for your quick reply! I understand the transformation but I am unsure on how to set sgn(j) and sgn(k). If from my original hamiltonian I don't have those qubits, how do I know the values of sgn(j) or sgn(k)? Thank you in advance!!! $\endgroup$
    – bjail66
    Commented Aug 6, 2021 at 8:05

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