Eastin–Knill theorem

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". 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.

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 or many-body theory.

The theorem is named after Bryan Eastin and Emanuel Knill, who published it in 2009.