Carrying out Magic State Cultivation using d=3 color code and d=5 surface code

Carrying out Magic State Cultivation using d=3 color code and d=5 surface code Ask Question Asked yesterday Modified yesterday Viewed 42 times 0 I am trying to simulate MSC (Magic State Cultivation) using an initial color code with distance 3 and the escape stage being carried out to a distance 5 surface code (why?). In Gidney's original MSC paper: "Magic state cultivation: growing T states as cheap as CNOT gates", there is code for constructing the circuits end-to-end (the full injection, cultivation and escaping to matchable code stages). Yet there is a constraint in there that dsurface >= 2 * dcolor. However, in Google's experimental paper: "Magic state cultivation on a superconducting quantum processor" on MSC they escape to a grafted code where the surface code had d=5. Yet they did not convert into a matchable code as it was "out of scope". My question is: is there a way to construct MSC where you start with dcolor=3 and then escape to dsurface=5 AND convert it into a matchable code? Is there a straightforward way to come up with the circuits that do this? If not, what prevents this? Final matchable code from Gidney's original paper (different shades of gray correspond to X and Z stabilizers): Grafted code in Google's experimental paper from Figure. 4 (colors correspond to color code stabilizers and gray as before): error-correctioncircuit-constructionmagic-states Share Improve this question Follow edited yesterday asked yesterday PrimeSoup 334 4 bronze badges Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 0 My question is: is there a way to construct MSC where you start with dcolor=3 and then escape to dsurface=5 AND convert it into a matchable code? Yes, see figure 11 of the magic state cultivation paper. All you have to do is drop some of the stabilizers and split some of them into pieces: Is there a straightforward way to come up with the circuits that do this? The straightforward way to do it would be to skip grafting in the first place by making a better color code decoder that supported soft information, and then just grow the color code directly. If not, what prevents this? For scale, most injection papers (experiment and theory) don't include growing the code at all. It's a lot more work to do. For cultivation, the difficulty peaks during the grafted code bit so we wanted to make sure we at least did that. The matcheable code is less scary, so we didn't bother. Just think of it as a token gesture towards the escape stage. By the way, stopping at the high distance matcheable code in the cultivation theory paper was also an effort-vs-benefit compromise. The truly end-to-end test would also consumes the state in order to rotate a logical qubit. Preparation and consumption can have funny ways of interacting where they can't get too close to each other (e.g. figure 14 of https://arxiv.org/pdf/2302.07395 ), so that end-to-end test could in fact reveal things you need to know in order to get the cost and fidelity right. So I wish people would start doing end-to-end rotation sims, and hopefully in the future we can also do end-to-end rotation experiments. Share Improve this answer Follow answered yesterday Craig Gidney 51.7k1 1 gold badge 54 54 silver badges 135 135 bronze badges Ok I see so it wasn't that producing the matchable code was difficult but rather easy enough to ignore. Follow up question: if it is easy to make the matchable code at dsurface=5 why can't you perform this in the code associated with the paper? It prevents this with the dsurface < dcolor * 2 condition and if I try to take it out I get errors with dcolor=3 and dsurface=5 –  PrimeSoup Commented yesterday @PrimeSoup for the theory paper I was focused on large distance escapes so I didn't put effort into making sure the barely-larger cases worked, and asserted those cases away in case they didn't work –  Craig Gidney Commented yesterday Thanks, do you know or have a feel of what would need to be changed? Do you see any reason why the dropped and split stabilizer decompositions of the color code portion would have to be changed? Still a bit confused as to how those decompositions are found, is it trial and error with the stabilizer flows? –  PrimeSoup Commented yesterday @primeSoup one solution is, within the color code area, switch to the instantaneous stabilizer group of a honeycomb code. There's lots of solutions. –  Craig Gidney Commented 21 hours ago 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 error-correctioncircuit-constructionmagic-states See similar questions with these tags. The Overflow Blog The find out stage of AI is just supply chain and password... Best of the Heap: First post of the... 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