The Eastin-Knill theorem is commonly paraphrased as 'no error correcting code has a universal set of transversal gates,' but this is a subtle misstatement. Using the 15-qubit quantum Reed-Muller code, it's shown that a universal gate set (Clifford+T) can be synthesized from transversal gates including X, T, MX, MZ, and CX. However, the catch is that the MX gate destroys Z-basis stabilizers, meaning it cannot be freely composed with other transversal gates without intermediate stabilizer recovery rounds. This makes MX only 'conditionally transversal.' The actual Eastin-Knill theorem states that no code can have a continuous symmetry acting transversely — which is crucially different from the popular claim. Gate decompositions involving dissipative gates and ancilla qubits can be universal without violating this. The post (published April 1st) uses this as a playful but technically rigorous exploration of the theorem's precise meaning.
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