Eastin–Knill theorem
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The Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits".[1] In other words, no quantum error correcting code can transversely implement a universal gate set, where a transversal logical gate is one that can be implemented on a logical qubit by the independent action of separate physical gates on corresponding physical qubits.[citation needed]
In addition to investigating fault tolerant quantum computation, the Eastin–Knill theorem is also useful for studying quantum gravity via the AdS/CFT correspondence and in condensed matter physics via quantum reference frame[2] or many-body theory.[3]
The theorem is named after Bryan Eastin and Emanuel Knill, who published it in 2009.[1]