Universal transversal gates

• URL: http://arxiv.org/abs/2410.07045v1
• Date: Wed, 9 Oct 2024 16:34:47 GMT
• Title: Universal transversal gates
• Authors: Pragati Gupta, Andrea Morello, Barry C. Sanders,
• Abstract summary: A long-standing challenge in quantum error correction is the infeasibility of universal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model. We present a code construction using~$n$~$d$-dimensional systems that changes the logical error probability from a lower bound~$ \Omega(\nicefrac{1}{n\log d})$ to an upper bound~$\mathcal O (\nicefrac{1}{n d})$ and allows exact correction of both local and correlated errors. Our universality condition determines the existence of a universal gate set for any quantum error-correcting code.

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