Why does the single-shot error correction with 3D gauge color codes save qubits or times?

Why does the single-shot error correction with 3D gauge color codes save qubits or times? Ask Question Asked 3 years, 2 months ago Modified today Viewed 130 times 0 I read about single-shot error correction using 3D gauge color codes. I saw the claim that it enables significant qubit and time overhead improvement regarding 2D surface codes, since it does not require several syndrome-measurements. However, since this gauge color code is already a 3D structure, just as the 2+1D of surface code with repeating syndrome measurement, why does it save qubits or time? error-correction Share Improve this question Follow edited Jan 24, 2023 at 17:31 glS♦ 28.1k7 7 gold badges 43 43 silver badges 140 140 bronze badges asked Jan 24, 2023 at 14:22 Yaron Jarach 8904 4 silver badges 11 11 bronze badges Add a comment 2 Answers Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 1 Well, it can save time, since you can (in principle) perform all the syndrome measurements in parallel. But as you point out, it does not obviously save in (space × × time). Share Improve this answer Follow answered Jan 24, 2023 at 17:00 squiggles 1,2807 7 silver badges 11 11 bronze badges Add a comment 0 There are multiple trade-offs at play. A 3D space-like volume should scale with O( d 3 ) 𝑂 ( 𝑑 3 ) and require O(1) 𝑂 ( 1 ) syndrome-extraction rounds, since it is single-shot decodable. A 2+1D will require O( d 2 ) 𝑂 ( 𝑑 2 ) qubits and O(d) 𝑂 ( 𝑑 ) syndrome-extraction rounds to correct for measurement errors. The space-time volume of both indeed scales the same, i.e., with O( d 3 ) 𝑂 ( 𝑑 3 ) . But there's more sauce to it if you look beyond their properties as quantum memories only. Namely, a 3D gauge colour code admits a transversal T ¯ ¯ ¯ ¯ 𝑇 ¯ gate, enabling dimensional-jumping protocols and giving you more to think about regarding resource trade-offs for universal fault-tolerance. (see https://arxiv.org/abs/1412.5079) Share Improve this answer Follow answered 30 mins ago Ramos 11 1 bronze badge 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 error-correction See similar questions with these tags. 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