Demonstration of fault-tolerant universal quantum gate operations.

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error-correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design, which, in general, increases the complexity of the implementation.