What quantum gate is XNOR equivalent to?

What quantum gate is XNOR equivalent to? Ask Question Asked 7 years, 6 months ago Modified today Viewed 1k times 2 The standard way to implement a reversible XOR gate is by means of a controlled-NOT gate or CNOT; this is the "standard quantum XOR operation". Physics.Stackexchange Is there a "standard quantum XNOR operation"? The XNOR gate (sometimes ENOR, EXNOR or NXOR and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. Wikipedia Alternatively, what is the logical complement of the CNOT gate? gate-synthesisuniversal-gatesquantum-gatefoundations Share Improve this question Follow edited Oct 1, 2018 at 1:21 asked Oct 1, 2018 at 1:00 user820789 3,44014 14 silver badges 47 47 bronze badges Add a comment 2 Answers Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 4 There is no "standard" method to implement XNOR, but it can be logically obtained by attaching a NOT gate (often called an X gate in quantum computing) to a logical XOR (which you know is implemented using CNOT). The X gate is applied to the target qubit of the CNOT. To answer your question more directly, there is no standard "quantum gate" that is equivalent to XNOR. The best way to implement XNOR in a quantum circuit is with a CNOT and an X on the second qubit. The reason why {CNOT,X} can give you a logical XNOR was explained in this answer to your own question 3.5 months ago. Share Improve this answer Follow edited Oct 1, 2018 at 1:20 answered Oct 1, 2018 at 1:14 user1271772 No more free time 14.6k2 2 gold badges 30 30 silver badges 79 79 bronze badges cNOT⋅(1⊗X) cNOT ⋅ ( 1 ⊗ 𝑋 ) ? What would the circuit look like (not sure which qubit would get the x)? Also, would it be accurate to call this 'gate' not CNOT? –  user820789 Commented Oct 1, 2018 at 1:22 1 Yes that is correct! :) –  user1271772 No more free time Commented Oct 1, 2018 at 1:22 I would like to update this question to more accurately ask the question I haven't figured out how to succinctly articulate in a meaningful way & am wondering if perhaps you could advise, as you have already taken time to provide an answer. I had asked in the comments of the initial XNOR question about SWAP. Upon further reflection however, I'm not sure that is correct. I have also learned since that time that XOR == "Symmetric Difference" & XNOR == "Logical Biconditional." "Quantum Symmetric Difference" & "Quantum Logical Biconditional" both yield less than 5 results in Google.. –  user820789 Commented Oct 6, 2018 at 3:37 I also have been looking into quantum, vector & fuzzy logics (De Morgan's laws seem to keep popping up a lot as well). The concepts of equality & equivalence also are recurrent. As you seem very versed in maths & quantum, perhaps you can understand what it is I am after, &/or identify the gaps in my current thinking & make a suggestion on what area(s) of math/quantum to focus on (has been on set/type theory + complexity classes; very interested in optical computing as well) in my continuing education. Thank you again for taking the time to provide so many great answers; I appreciate it! –  user820789 Commented Oct 6, 2018 at 3:55 Add a comment 0 Using 2 CNOTS in parrallel should make the output a XNOR of the inputs ( A, B ). The box is the qubit being measured, and is measuring the XNOR of A and B. This version doesn't change the original values of A or B, and retains them for future use. Share Improve this answer Follow answered 31 mins ago Zamiul Haque 1 New contributor Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions gate-synthesisuniversal-gatesquantum-gatefoundations See similar questions with these tags. 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