The CNOT gate is usually written as

$|0\rangle\langle0|\otimes I + |1\rangle\langle1|\otimes X$

(with $X,Y,Z$ beign the Pauli Basis and $I$ the Identity).

I have yet to stumble across the representation Wikipedia gives when looking at books on the topic:


How can I show these forms are equivalent? Where can I find a derivation that shows this?

Cross-posted on qc.SE

  • $\begingroup$ Maybe ask in quantumcomputing.stackexchange.com $\endgroup$
    – Mauricio
    Commented May 18, 2022 at 9:36
  • $\begingroup$ Thank you for the hint! $\endgroup$
    – manuel459
    Commented May 18, 2022 at 9:44
  • 1
    $\begingroup$ There might be a $\otimes$ missing in the argument of the exponential $\endgroup$
    – Mauricio
    Commented May 18, 2022 at 10:01
  • $\begingroup$ Thank you. That is absolutely right. $\endgroup$
    – manuel459
    Commented May 18, 2022 at 10:04


Your Answer

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