How to measure logical Y in Surface code?

How to measure logical Y in Surface code? Ask Question Asked 3 days ago Modified 3 days ago Viewed 111 times 1 How do you measure the logical Y observable in a surface code? In some papers I've seen that code deformations are needed and other complex circuits of moving twists around. But in Gidney's code in the "Magic state cultivation: growing T states as cheap as CNOT gates" paper I just see the standard stabilizer detectors and an observable consisting of an MPP in shape below with a combination of the bottom right corner is a Y Pauli, the black line represents the logical Z Paulis and the green line represents the logical X Paulis. What is the justification of this being the logical Y measurement? I loosely understand that Y = iXZ but it doesn't seem like enough of a justification. (figure from the paper: "Suppressing quantum errors by scaling a surface code logical qubit") error-correctionsurface-codetopological-quantum-computinglogical-observables Share Improve this question Follow asked Jun 24 at 9:15 PrimeSoup 594 4 bronze badges Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 1 See the paper "Inplace Access to the Surface Code Y Basis" Topologically speaking, what you need to do is fuse the twists at the corners of the surface code patch diagonally across the patch: In terms of the circuit, the key round is the one that's performing a domain wall on half of the patch while not doing that on the other half: Share Improve this answer Follow answered Jun 24 at 9:24 Craig Gidney 51.9k1 1 gold badge 54 54 silver badges 139 139 bronze badges Ok I roughly went through this paper but is this what is being done to measure the S|+> state in the MSC paper? It seems different but maybe it's just the superficial details of no Hadamards and clean split between top right and bottom left corners in the MSC circuit. –  PrimeSoup Commented Jun 24 at 9:46 @PrimeSoup In the cultivation paper, it's just measured by turning off the simulated noise and directly accessing the operator. On hardware you can't get away with stuff like that, but for a theory paper it massively simplifies things. –  Craig Gidney Commented Jun 24 at 10:54 I see, ok this feels somewhat basic but then I am a bit confused why it is so different when you want to measure it fault tolerantly. In the beginning of the paper you referenced it seems to say because the Y logical isn't transversal but I don't see why that's such an issue in this case. –  PrimeSoup Commented Jun 24 at 12:13 @PrimeSoup most things are harder when you add the requirement that it be fault tolerant –  Craig Gidney Commented 2 days 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-correctionsurface-codetopological-quantum-computinglogical-observables See similar questions with these tags. The Overflow Blog Code isn’t the only thing causing your production... Paging Charity! How can engineering leaders avoid becoming Bond... 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