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^1,2. 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^3-5, which, in general, increases the complexity of the implementation. Here we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by the use of auxiliary flag qubits^6-10. We perform a logical two-qubit controlled-NOT gate between two instances of the seven-qubit colour code^11,12, and fault-tolerantly prepare a logical magic state^8,13. We then realize a fault-tolerant logical T gate by injecting the magic state by teleportation from one logical qubit onto the other¹⁴. We observe the hallmark feature of fault tolerance-a superior performance compared with a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error-correction cycles^15,16, these results provide a route towards error-corrected universal quantum computation.