Quantum gates reversibility

Quantum gates reversibility Ask Question Asked 11 days ago Modified 11 days ago Viewed 87 times 1 The Reversibility of the quantum gates output to input is basically because of the extra bit (ancilla qubit) used and is by design and not naturally. The same can be done in classical also to reverse the output to input. Please let me know if my understanding is correct on reversibility. In that case if the circuit has multiple inputs should we also have matching ancilla qubit? quantum-gatequantum-algorithms Share Improve this question Follow edited May 25 at 7:46 Martin Vesely 15.6k4 4 gold badges 34 34 silver badges 77 77 bronze badges asked May 25 at 6:32 mysran 211 1 bronze badge Hi and welcome to Quantum Computing SE. Any quantum gate is described by a unitary matrix which is invertible. Hence any quantum gates in reversible naturally. Only exceptions are measurement and reset gates which cannot be reversed. –  Martin Vesely Commented May 25 at 7:45 Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 1 Reversibility of quantum gates isn't a design choice, but a need to have gates governed by quantum evolution, which is reversible (about why, you can check: https://physics.stackexchange.com/questions/270266/why-do-quantum-gates-have-to-be-reversible) Reversibility implies having an one-to-one relation between gate inputs and outputs, otherwise you would destroy information and would not be able to go "backward" (saying it in a bad way: if two different inputs result in the same output, given the output and going back you wouldn't know which input to get, you would miss injective property) Considering domain and range dimensions, one-to-one relation leads to gates having the same number of inputs and outputs lines. The ancilla can naively be seen as a trick to represent a QUANTUM GATE using CLASSICAL well-known logical gates, but be careful, it's usefulness is more profound than simply making the number of inputs = the number of outputs: in gates just more complex than the ones reproducing quantum version of their classical counterparts, we can have many ancillas and they can be seen as memory where to store intermediate results, before the final one, to avoid discarding anything (remember: discard = erasing = information lost = irreversibility). Note two important things: once the gate is evaluated, you cannot simply disinterest yourself of intermediate results because it would mean again to fall into irreversibility. That's why you have, for example, to "uncompute" meaning to apply the gate backward to revert to 0 (the ancillas' initial values) the intermediate store memory Between "computing" and "uncomputing" (to be read as "after computing" and "before uncomputing") you have your gate result, but of course you have to be careful "reading" it to avoid state collapse (which you cannot afford because because you still have to uncompute): that's where other ancilla(s) appears, as "service line(s)" to to read gate output value in a not destructively way. So, trying to understand and answer to your closing question, number of ancillas is related to dimension of output and intermediate results not to input cardinality (even because I believe that in more advanced designs ancillas can be reused) Share Improve this answer Follow answered May 25 at 8:11 baro77 1916 6 bronze badges 1 Thanks for the clarification –  mysran Commented May 27 at 5:10 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 quantum-gatequantum-algorithms See similar questions with these tags. The Overflow Blog What it takes to be a player in the international AI... Making the OWASP top ten in the vibe code... 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