2
$\begingroup$

Sorry if this question sounds too basic. But I can't find a word for those quantum gates than can be reversed (exchanging the target qubit with the control qubit) and still performs the same operation. Such as the CPhase or the SQSWAP.

I don't think they can be called "reversibles", because that means another thing.

Any ideas?

Improve this question
$\endgroup$
1
  • $\begingroup$ "Swap-Covariant"? (I.e., they commute with the swap operation.) $\endgroup$
    – Norbert Schuch
    Commented Mar 10, 2021 at 19:00

4 Answers 4

Reset to default
7
$\begingroup$

symmetric?

Again, can be used in other contexts, but it is the right word for this context because what you're talking about is something that's invariant under swap. Perhaps the first time you use it, one should clarify with the phrase "symmetric under exchange of the inputs".

Improve this answer
$\endgroup$
2
$\begingroup$

All quantum gates are reversible, in the sense that they always admit an inverse which is a quantum gate as well. This comes from the fact that quantum gates are (usually) required to be unitary.

What you probably meant to ask is how you call gates $U$ such that $U^2=I$. If you assume $U$ is unitary, that is $U^\dagger U=UU^\dagger=I$, then this is equivalent to the condition $U^\dagger =U$. Such gates are called Hermitian (or symmetric when they are real).

If, instead, you are referring to gates whose action is invariant under exchange of the inputs, then that can mean gates $U$ such that $U|a,b\rangle=U|b,a\rangle$ for all one-qubit states $|a\rangle$ and $|b\rangle$. This essentially means that the two middle columns of the matrix (in the standard choice of canonical basis) are the same. Yet another possible interpretation is that the matrix is required to have the same description when exchanging both the two input qubits and the two output qubits. This amounts to asking for $U$ to commute with the swap operation: $[U,\mathrm{SWAP}]=0$. You can compute explicitly the form of these matrices, but I don't think there is any universally accepted special name for these sorts of operations.

Improve this answer
$\endgroup$
9
  • 1
    $\begingroup$ That's what I thought was being asked when I first read the question. I don't think it is though. $\endgroup$
    – DaftWullie
    Commented Sep 5, 2019 at 15:59
  • $\begingroup$ @DaftWullie why not? "can be reversed and still perform the same operation" reads to me as asking for gates such that $U^{-1}=U^\dagger=U$ $\endgroup$
    – glS ♦
    Commented Sep 5, 2019 at 16:10
  • $\begingroup$ but it is then clarified that the reversal means "exchanging the target qubit with the control qubit" $\endgroup$
    – DaftWullie
    Commented Sep 5, 2019 at 16:11
  • 1
    $\begingroup$ @MarkS you mean because it satisfies every single one of the conditions, or because I missed that it doesn't satisfy one of them? $\endgroup$
    – glS ♦
    Commented Sep 5, 2019 at 18:10
  • 2
    $\begingroup$ @Alex personally I would find that a very confusing notation. "Symmetric" is used for matrices such that $A^T=A$. Something like symmetric under exchange of inputs might be better. $\endgroup$
    – glS ♦
    Commented Sep 5, 2019 at 20:59
-1
$\begingroup$

One might consider this to be equivalent to the definition of a unitary transformation. All quantum gates are reversible, thus all quantum gates are unitary.

Improve this answer
$\endgroup$
-3
$\begingroup$

They are called quantum Unitary gates. For the Unitary gates $UU^{\dagger}=U^{\dagger}U=I$ where $U^{\dagger}$ is the adjoint of $U$ . See this link for more information: https://en.wikipedia.org/wiki/Unitary_operator

Improve this answer
$\endgroup$

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.