Is the five-qubit code magic state distillation protocol along with Clifford gates sufficient for universal quantum computation?

Is the five-qubit code magic state distillation protocol along with Clifford gates sufficient for universal quantum computation? Ask Question Asked today Modified today Viewed 11 times 0 In the original paper on magic state distillation https://arxiv.org/pdf/quant-ph/0403025, the 5-to-1 distillation circuit is used to implement a π/6 phase rotation. Is this distillation protocol, along with Clifford gates, sufficient for universal quantum computation? If so, why is the 15-to-1 the commonly cited protocol for universal fault-tolerant quantum computation? error-correctionfault-tolerancemagic-states Share Improve this question Follow asked 2 hours ago Noobintrouble 1 New contributor Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 1 The problem is that the state produced by 5-to-1 distillation (which they call the T state in this particular paper) has to be transformed into a different single qubit state before it can be used, and this transformation costs 3 of the states. From the paper you cited: Additionally, the resulting state produces an amount of rotation that's harder to work with (e.g. it makes it more expensive to synthesize a Toffoli gate). Whereas the 15-to-1 protocol distills |0⟩+ i √ |1⟩ | 0 ⟩ + 𝑖 | 1 ⟩ states of which only 4 are needed to do a Toffoli. Additionally, the 15-to-1 protocol gets cubic suppression instead of quadratic suppression. So the comparison is not as bad as it initially looks. And there's a 10-to-2 protocol with quadratic suppression for |0⟩+ i √ |1⟩ | 0 ⟩ + 𝑖 | 1 ⟩ as a fallback. And the catalyzed 8-to-1 factory that just has a straight up better rate than 5-to-1. And the 8-to-CCZ factory for when you need a bit more suppression but know you're going to be doing a Toffoli. So, yes, 5-to-1 distillation is sufficient... but it isn't efficient. Share Improve this answer Follow edited 1 hour ago answered 1 hour ago Craig Gidney 51.2k1 1 gold badge 53 53 silver badges 133 133 bronze badges Thanks a lot for your answer! –  Noobintrouble Commented 1 hour 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. 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