Magic state distillation

Magic state distillation is a technique used in quantum computing to produce highly accurate quantum states, called magic states, from multiple noisier copies of those states. The method was first proposed by Emanuel Knill in 2004 and was further developed and analyzed by Sergey Bravyi and Alexei Kitaev in a 2005 paper. It addresses a core limitation described by the Gottesman-Knill theorem: operations drawn only from the Clifford group can be simulated efficiently on a classical computer, so a quantum computer needs access to non-Clifford resources to achieve any advantage over classical computation and to support universal quantum computation. Magic state distillation supplies that resource by taking many imperfect copies of a magic state and combining them through a distillation protocol to produce fewer copies of much higher fidelity. Combined with the otherwise classically simulable Clifford gates, these distilled magic states allow a fault tolerant quantum computer to implement the additional gates needed for universal computation. The technique has also been connected to quantum contextuality, a property some researchers regard as contributing to the computational advantage of quantum computers, and multiple improved distillation routines with different resource trade offs have since been developed.