Universal transversal gates
Pragati Gupta, Andrea Morello, Barry C. Sanders

TL;DR
This paper establishes a necessary and sufficient condition for quantum codes to have universal transversal gates, overcoming the Eastin-Knill no-go theorem in certain error models, and introduces a new code construction with improved error correction capabilities.
Contribution
It provides a general condition for universal transversal gates and presents a novel code construction that corrects local and correlated errors more effectively.
Findings
The Eastin-Knill theorem does not hold for all error models.
A new code construction reduces logical error probability from to .
The universality condition determines the existence of universal gate sets for quantum codes.
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 -dimensional systems that changes the logical error probability from a lower bound to an upper bound 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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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Complexity and Algorithms in Graphs · Quantum Information and Cryptography
