In quantum circuit, how do you implement the rotation of multi-body interaction, such as $e^{-i\theta\sigma_z^1\sigma_z^2\sigma_z^3}$? I already know the case of less than two-body interaction, but I cannot find any textbook about more than three-body interaction.

  • $\begingroup$ You may refer to answer given here $\endgroup$
    – Omkar
    Apr 9, 2020 at 4:30
  • $\begingroup$ @Omkar Thank you very much $\endgroup$
    – sotowa
    Apr 13, 2020 at 3:36

1 Answer 1


Here's an image from a previous answer of mine: enter image description here If you replace the $\sigma_1\otimes\sigma_2\otimes\ldots\otimes\sigma_n$ with the tensor product of operators that you want (a single tensor product; a sum of terms needs some extra techniques based on, at its most simplistic, a Trotter expansion), and set the phase of the phase gate, $t$ equal to $-2\theta$, this will do the job up to a global phase.

Basically, what the circuit does is it entangles the register with the ancilla such that the ancilla is in the state 0/1 or the other register is in a +1 or -1 eigenstate of the operator respectively. That means you can use the ancilla to decide if you need to acquire a phase, before undoing the entanglement.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.